Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61488 |
| 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 | |
1788 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)(24,33)(25,37)(26,31)(27,32)(28,41)(29,36)(30,38)(34,49)(35,45)(39,46)(40,44)(42,47)(43,50)(48,52)(51,53);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,34)(26,40)(27,36)(28,35)(30,43)(31,45)(32,33)(37,53)(38,52)(39,51)(41,44)(42,50)(46,49)(47,48);(22,25,27,39)(23,30,32,47)(24,34,36,51)(26,38,28,42)(29,43,33,48)(31,46,41,37)(35,50,40,52)(44,53,45,49);(15,18)(19,21)(22,26,27,28)(23,31,32,41)(24,35,36,40)(25,38,39,42)(29,44,33,45)(30,46,47,37)(34,50,51,52)(43,53,48,49);(14,16,17,20)(15,19,18,21)(24,36)(29,33)(34,51)(35,40)(43,48)(44,45)(49,53)(50,52)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54476);