Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61492 |
| 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 | |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
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)(24,29)(25,37)(26,31)(27,41)(28,32)(30,39)(33,49)(34,44)(35,45)(36,51)(38,53)(40,47)(42,48)(43,50)(46,52);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,38)(26,34)(27,36)(28,35)(30,46)(31,44)(32,45)(33,40)(37,53)(39,52)(41,51)(42,50)(43,48)(47,49);(22,25)(23,30)(24,33)(26,39)(27,42)(28,40)(29,43)(31,47)(32,48)(34,50)(35,38)(36,52)(37,41)(44,53)(45,46)(49,51);(15,18)(19,21)(22,26,28,27)(23,31,32,41)(24,34,35,36)(25,39,40,42)(29,44,45,51)(30,47,48,37)(33,50,38,52)(43,53,46,49);(14,16,17,20)(15,19,18,21)(24,35)(29,45)(33,38)(34,36)(43,46)(44,51)(49,53)(50,52)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54480);