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×#33681 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
532 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)(16,19)(17,18)(20,21)(24,32)(25,35)(26,37)(28,40)(30,45)(31,44)(33,50)(34,49)(36,39)(38,48)(41,52)(42,53)(43,51)(46,47);(15,18)(19,21)(22,23)(24,28)(25,30)(26,31)(27,29)(32,40)(33,42)(34,41)(35,45)(36,46)(37,44)(38,43)(39,47)(48,51)(49,52)(50,53);(22,24,27,34)(23,28,29,41)(25,36,38,50)(26,39,37,33)(30,46,43,53)(31,47,44,42)(32,48,49,35)(40,51,52,45);(14,16,17,20)(15,19,18,21)(23,29)(28,41)(30,43)(31,44)(40,52)(42,47)(45,51)(46,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26669);