Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33494 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C24 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C23×C8 |
| prime radical | C13×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
556 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 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)(22,23,25,30,26,31,36,44,27,32,37,45,38,46,49,53)(24,28,34,39,35,40,48,50,33,29,41,42,47,43,51,52);(14,16)(15,18)(17,21)(19,20)(22,24)(23,28)(25,34)(26,35)(27,33)(29,32)(30,39)(31,40)(36,48)(37,41)(38,47)(42,45)(43,46)(44,50)(49,51)(52,53);(16,21)(18,20)(22,24)(23,29)(25,34)(26,35)(27,33)(28,32)(30,42)(31,43)(36,48)(37,41)(38,47)(39,45)(40,46)(44,52)(49,51)(50,53);(15,19)(18,20)(24,33)(28,29)(34,41)(35,47)(39,42)(40,43)(48,51)(50,52)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26482);