Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18315 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
868 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,23)(17,21)(18,26)(19,22)(20,24)(25,28)(27,29)(30,31,35,39)(32,36,42,49)(33,37,44,51)(34,45,46,38)(40,52,54,47)(41,55,56,48)(43,57,58,50)(53,59,61,60);(14,16)(15,20)(17,24)(18,27)(19,25)(21,28)(22,29)(23,26)(30,32)(31,36)(33,40)(34,41)(35,42)(37,47)(38,48)(39,49)(43,53)(44,54)(45,55)(46,56)(50,59)(51,52)(57,60)(58,61);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(30,33)(31,37)(32,40)(34,43)(35,44)(36,47)(38,50)(39,51)(41,53)(42,54)(45,57)(46,58)(48,59)(49,52)(55,60)(56,61);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(30,34,35,46)(31,38,39,45)(32,41,42,56)(33,43,44,58)(36,48,49,55)(37,50,51,57)(40,53,54,61)(47,59,52,60)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11303);