Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #33982 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33984 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×D16 |
| commutator, Frattini, cosocle | C16 | C24×C13 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C13×#41 ◁ C13×#131 ◁ C13×#504 ◁ G | |
452 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,21,27)(16,28,33,70)(17,23,34,55)(18,38,43,67)(19,44,47,100)(20,48,46,26)(22,50,54,30)(24,59,62,41)(25,63,65,40)(29,68,71,120)(31,76,77,117)(32,78,49,69)(35,82,79,119)(36,87,80,128)(37,89,81,58)(39,64,95,118)(42,98,97,92)(45,60,101,116)(51,102,103,72)(52,99,106,94)(53,75,66,93)(56,109,107,85)(57,112,108,84)(61,96,91,115)(73,124,122,141)(74,125,90,121)(83,113,126,139)(86,135,127,131)(88,110,129,138)(104,136,137,133)(105,123,114,132)(111,134,130,140);(14,16,21,33)(15,22,27,54)(17,29,34,71)(18,39,43,95)(19,45,47,101)(20,49,46,32)(23,51,55,103)(24,60,62,116)(25,64,65,118)(26,66,48,53)(28,67,70,38)(30,59,50,41)(31,63,77,40)(35,83,79,126)(36,88,80,129)(37,90,81,74)(42,99,97,94)(44,52,100,106)(56,110,107,138)(57,113,108,139)(58,114,89,105)(61,117,91,76)(68,119,120,82)(69,92,78,98)(72,109,102,85)(73,112,122,84)(75,96,93,115)(86,136,127,133)(87,104,128,137)(111,141,130,124)(121,131,125,135)(123,134,132,140);(14,17)(15,23)(16,29)(18,35)(19,36)(20,37)(21,34)(22,51)(24,56)(25,57)(26,58)(27,55)(28,68)(30,72)(31,73)(32,74)(33,71)(38,82)(39,83)(40,84)(41,85)(42,86)(43,79)(44,87)(45,88)(46,81)(47,80)(48,89)(49,90)(50,102)(52,104)(53,105)(54,103)(59,109)(60,110)(61,111)(62,107)(63,112)(64,113)(65,108)(66,114)(67,119)(69,121)(70,120)(75,123)(76,124)(77,122)(78,125)(91,130)(92,131)(93,132)(94,133)(95,126)(96,134)(97,127)(98,135)(99,136)(100,128)(101,129)(106,137)(115,140)(116,138)(117,141)(118,139);(17,34)(23,55)(29,71)(35,79)(36,80)(37,81)(51,103)(56,107)(57,108)(58,89)(68,120)(72,102)(73,122)(74,90)(82,119)(83,126)(84,112)(85,109)(86,127)(87,128)(88,129)(104,137)(105,114)(110,138)(111,130)(113,139)(121,125)(123,132)(124,141)(131,135)(133,136)(134,140)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26972);