Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61655 |
| 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×#525 ◁ G | |
2032 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)(14,15)(16,20)(17,19)(18,21)(22,23)(24,29)(25,36)(26,32)(27,40)(28,31)(30,37)(33,48)(34,45)(35,43)(38,47)(39,44)(41,46)(42,51)(49,53)(50,52);(14,16)(15,18)(17,21)(19,20)(22,24,28,34)(23,29,31,45)(25,33,38,49)(26,39,27,35)(30,42,46,52)(32,44,40,43)(36,48,47,53)(37,51,41,50);(22,25)(23,30)(24,33)(26,37)(27,41)(28,38)(29,42)(31,46)(32,47)(34,49)(35,50)(36,40)(39,51)(43,48)(44,53)(45,52);(16,21)(18,20)(23,31)(24,34)(30,46)(32,40)(33,49)(35,39)(36,47)(50,51);(15,19)(18,20)(22,26,28,27)(23,32,31,40)(24,35,34,39)(25,37,38,41)(29,43,45,44)(30,47,46,36)(33,50,49,51)(42,48,52,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54643);