Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10466 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,20)(19,21)(22,23)(24,33)(25,38)(26,43)(27,31)(28,32)(29,35)(30,41)(34,49)(36,45)(37,48)(39,44)(40,47)(42,52)(46,51)(50,53);(22,24,28,37)(23,29,32,45)(25,39,41,50)(26,36,27,35)(30,46,38,49)(31,48,43,33)(34,40,51,42)(44,52,53,47);(15,18)(16,21)(19,20)(22,25,26,40,28,41,27,42)(23,30,31,47,32,38,43,52)(24,34,35,50,37,51,36,39)(29,44,33,46,45,53,48,49)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3454);