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×#33680 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
534 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)(22,23,27,32)(24,28,33,41)(25,29,38,45)(26,39,37,31)(30,46,44,36)(34,40,47,51)(35,50,48,43)(42,53,52,49);(15,18)(19,21)(22,24,27,33)(23,28,32,41)(25,34,38,47)(26,35,37,48)(29,40,45,51)(30,42,44,52)(31,43,39,50)(36,49,46,53);(23,29)(25,36)(26,37)(28,40)(30,31)(32,45)(34,49)(35,48)(38,46)(39,44)(41,51)(42,43)(47,53)(50,52);(14,16,17,20)(15,19,18,21)(24,33)(28,41)(34,47)(35,48)(40,51)(42,52)(43,50)(49,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26668);