Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33538 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×#447 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1088 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,28)(17,33)(18,24)(19,39)(20,26)(21,27)(22,31)(23,36)(25,41)(29,57)(30,55)(32,56)(34,49)(35,66)(37,53)(38,52)(40,45)(42,51)(43,50)(44,71)(46,70)(47,62)(48,69)(54,60)(58,76)(59,63)(61,74)(64,68)(65,75)(67,73)(72,77);(14,16)(15,22)(17,29)(18,30)(19,40)(20,43)(21,32)(23,44)(24,45)(25,50)(26,46)(27,47)(28,39)(31,41)(33,63)(34,58)(35,67)(36,60)(37,61)(38,62)(42,70)(48,74)(49,73)(51,56)(52,55)(53,72)(54,64)(57,66)(59,68)(65,77)(69,71)(75,76);(14,17)(15,23)(16,29)(18,34)(19,35)(20,36)(21,37)(22,44)(24,33)(25,48)(26,53)(27,49)(28,54)(30,58)(31,59)(32,61)(38,65)(39,64)(40,67)(41,68)(42,69)(43,60)(45,63)(46,72)(47,73)(50,74)(51,75)(52,66)(55,57)(56,76)(62,77)(70,71);(14,18,21,20)(15,24,27,26)(16,30,32,43)(17,34,37,36)(19,38,42,41)(22,45,47,46)(23,33,49,53)(25,39,52,51)(28,55,56,50)(29,58,61,60)(31,40,62,70)(35,65,69,68)(44,63,73,72)(48,64,66,75)(54,57,76,74)(59,67,77,71)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26526);