Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33740 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| 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)(25,33)(26,36)(28,38)(30,39)(31,43)(34,48)(35,46)(37,47)(40,49)(41,53)(42,52)(44,45)(50,51);(15,18)(19,21)(22,23,27,29)(24,28,35,40)(25,30,37,42)(26,31,36,43)(32,38,46,49)(33,39,47,52)(34,41,44,50)(45,51,48,53);(22,24,33,45,26,34,37,46,27,35,47,48,36,44,25,32)(23,28,39,51,31,41,42,49,29,40,52,53,43,50,30,38);(14,16,17,20)(15,19,18,21)(23,29)(28,40)(30,42)(31,43)(38,49)(39,52)(41,50)(51,53)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26728);