Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33970 |
| 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 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G | |
528 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)(15,19)(20,21)(22,23)(24,33)(25,30)(26,29)(27,40)(28,34)(31,39)(32,38)(35,41)(36,43)(37,45)(42,51)(44,49)(46,53)(47,52)(48,50);(14,15,18,19)(16,20,17,21)(22,24,25,34)(23,28,30,33)(26,35,37,49)(27,36,38,50)(29,44,45,41)(31,42,46,47)(32,43,40,48)(39,52,53,51);(14,16,18,17)(15,20,19,21)(23,29)(24,34)(26,39)(27,38)(28,41)(30,45)(31,32)(33,44)(35,51)(37,53)(40,46)(42,48)(43,47)(49,52);(14,17,18,16)(15,20,19,21)(24,34)(28,33)(35,49)(36,50)(41,44)(42,47)(43,48)(51,52)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26958);