Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33628 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C23×C13 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
534 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)(14,15,17,19)(16,20,21,18)(22,23)(24,32)(25,36)(26,41)(27,29)(28,33)(30,39)(31,38)(34,52)(35,49)(37,47)(40,48)(42,46)(43,51)(44,53)(45,50);(14,16,17,21)(15,18,19,20);(22,24,27,35)(23,28,29,43)(25,37,40,53)(26,42,38,34)(30,46,45,52)(31,47,41,44)(32,48,49,36)(33,50,51,39);(23,29)(28,43)(30,45)(31,41)(32,49)(36,48)(44,47)(46,52)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26616);