Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33702 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
602 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)(23,29)(24,34)(25,26)(27,38)(31,42)(32,43)(33,47)(35,36)(37,49)(39,40)(41,45)(46,52)(48,50)(51,53);(15,18)(19,21)(22,23,26,32,27,33,39,42,28,31,40,47,38,43,25,29)(24,30,34,45,36,46,48,51,37,44,49,53,50,52,35,41);(14,16,17,20)(15,19,18,21)(22,24,25,35,38,50,40,49,28,37,39,48,27,36,26,34)(23,30,29,41,43,52,47,53,31,44,42,51,33,46,32,45);(23,31)(29,42)(30,44)(32,47)(33,43)(41,51)(45,53)(46,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26690);