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×#33890 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
562 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)(14,15,17,19)(16,20,21,18)(22,23,27,30)(24,28,33,41)(25,29,38,45)(26,39,37,32)(31,47,46,36)(34,44,48,40)(35,52,49,43)(42,50,53,51);(14,16)(15,18)(17,21)(19,20)(22,24)(23,28)(25,34)(26,35)(27,33)(29,44)(30,41)(31,42)(32,43)(36,51)(37,49)(38,48)(39,52)(40,45)(46,53)(47,50);(23,29)(24,33)(25,36)(26,37)(28,40)(30,45)(31,32)(34,50)(38,47)(39,46)(41,44)(42,52)(43,53)(48,51);(16,21)(18,20)(23,30)(28,41)(29,45)(31,46)(32,39)(40,44)(42,53)(43,52)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26878);