Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33678 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2184 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(16,19)(17,18)(20,21)(22,23)(24,28)(25,29)(26,39)(27,32)(30,36)(31,37)(33,41)(34,40)(35,49)(38,45)(42,48)(43,47)(44,50)(46,51)(52,53);(15,18)(19,21)(22,24)(23,28)(25,34)(26,35)(27,33)(29,40)(30,42)(31,43)(32,41)(36,48)(37,47)(38,46)(39,49)(44,52)(45,51)(50,53);(23,29)(25,36)(26,37)(28,40)(30,31)(32,45)(34,48)(35,47)(38,50)(39,44)(41,51)(42,43)(46,53)(49,52);(14,16,17,20)(15,19,18,21)(24,33)(28,41)(34,46)(35,47)(40,51)(42,52)(43,49)(48,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26666);