Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19060 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3553 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
822 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,22)(17,24)(19,27)(20,25)(23,26)(28,29)(30,31,36,41)(32,42,45,54)(33,46,47,55)(34,40,35,39)(37,49,52,44)(38,50,53,48)(43,51,57,61)(56,58,60,59);(14,15,18,21)(16,19,23,28)(17,25,24,20)(22,29,26,27)(30,32)(31,37)(33,43)(34,49)(35,44)(36,45)(38,51)(39,54)(40,42)(41,52)(46,60)(47,57)(48,59)(50,58)(53,61)(55,56);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,24)(25,27)(30,33)(31,38)(32,43)(34,48)(35,50)(36,47)(37,51)(39,46)(40,55)(41,53)(42,56)(44,58)(45,57)(49,59)(52,61)(54,60);(33,47)(38,53)(43,57)(46,55)(48,50)(51,61)(56,60)(58,59)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12048);