Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61501 |
| 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 | |
1800 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)(19,21)(22,23,27,32)(24,33,36,29)(25,37,40,48)(26,31,28,42)(30,43,49,39)(34,50,38,53)(35,46,41,45)(44,52,47,51);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,38)(26,41)(27,36)(28,35)(30,47)(31,46)(32,33)(34,40)(37,50)(39,51)(42,45)(43,52)(44,49)(48,53);(22,25)(23,30)(24,34)(26,39)(27,40)(28,43)(29,44)(31,48)(32,49)(33,47)(35,51)(36,38)(37,42)(41,52)(45,53)(46,50);(15,18)(19,21)(22,26,27,28)(23,31,32,42)(24,35,36,41)(25,39,40,43)(29,45,33,46)(30,48,49,37)(34,51,38,52)(44,53,47,50);(14,16,17,20)(15,19,18,21)(24,36)(29,33)(34,38)(35,41)(44,47)(45,46)(50,53)(51,52)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54489);