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×#33671 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
554 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)(16,19)(17,18)(20,21)(22,23)(24,34)(25,31)(26,32)(27,30)(28,42)(29,36)(33,41)(35,49)(37,48)(38,44)(39,46)(40,47)(43,52)(45,51)(50,53);(15,18)(19,21)(22,24,26,36)(23,29,32,34)(25,35,28,38)(27,37,40,52)(30,43,47,48)(31,44,42,49)(33,45,46,50)(39,51,41,53);(23,30)(25,28)(27,41)(29,43)(31,33)(32,47)(34,48)(35,38)(37,53)(39,40)(42,46)(44,45)(49,50)(51,52);(14,16,17,20)(15,19,18,21)(22,25,26,28)(23,31,32,42)(24,35,36,38)(27,39,40,41)(29,44,34,49)(30,46,47,33)(37,51,52,53)(43,50,48,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26659);