Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62091 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1776 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23)(24,34)(25,39)(26,33)(27,32)(28,31)(29,37)(30,40)(35,49)(36,44)(38,45)(41,47)(42,46)(43,52)(48,50)(51,53);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,35)(26,36)(27,37)(28,38)(30,43)(31,44)(32,34)(33,45)(39,53)(40,50)(41,51)(42,52)(46,48)(47,49);(22,25,27,41)(23,30,32,46)(24,35,37,51)(26,40,28,42)(29,43,34,48)(31,39,33,47)(36,50,38,52)(44,53,45,49);(15,18)(19,21)(22,26,27,28)(23,31,32,33)(24,36,37,38)(25,40,41,42)(29,44,34,45)(30,39,46,47)(35,50,51,52)(43,53,48,49);(14,16,17,20)(15,19,18,21)(23,32)(24,37)(30,46)(31,33)(35,51)(36,38)(39,47)(50,52)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55079);