Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33706 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
598 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)(24,36)(25,30)(26,44)(27,47)(28,48)(29,35)(31,38)(32,37)(33,46)(34,45)(39,51)(40,50)(41,49)(42,53)(43,52);(15,18)(19,21)(22,24,37,43,28,40,46,41,29,38,27,39,45,42,26,25)(23,30,44,53,34,51,47,31,35,49,33,50,48,52,32,36);(14,16,17,20)(15,19,18,21)(22,25,26,42,45,39,27,38,29,41,46,40,28,43,37,24)(23,31,32,51,48,53,33,30,35,36,47,52,34,50,44,49);(24,38)(25,41)(30,49)(31,36)(39,43)(40,42)(50,53)(51,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26694);