Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33540 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1078 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)(18,37)(19,27)(20,26)(21,24)(22,30)(23,35)(25,40)(29,56)(31,62)(32,55)(34,65)(36,52)(38,53)(39,49)(41,51)(42,47)(43,50)(44,71)(45,61)(46,69)(48,68)(54,58)(57,63)(59,76)(60,74)(64,67)(66,72)(70,75)(73,77);(14,16,21,32)(15,22,24,45)(17,29,36,60)(18,38,41,69)(19,31,20,43)(23,44,47,72)(25,50,49,62)(26,46,27,53)(28,51,55,37)(30,39,61,40)(33,63,52,73)(34,66,68,71)(35,58,42,59)(48,74,65,56)(54,75,76,64)(57,70,77,67);(14,17)(15,23)(16,29)(18,34)(19,42)(20,35)(21,36)(22,44)(24,47)(25,48)(26,52)(27,33)(28,54)(30,57)(31,59)(32,60)(37,64)(38,66)(39,70)(40,67)(41,68)(43,58)(45,72)(46,73)(49,65)(50,74)(51,75)(53,63)(55,76)(56,62)(61,77)(69,71);(15,24)(22,45)(23,47)(25,49)(26,27)(28,55)(33,52)(37,51)(44,72)(46,53)(48,65)(50,62)(54,76)(56,74)(63,73)(64,75)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26528);