Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23989 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1210 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)(16,20)(17,19)(18,21)(22,23)(24,28)(25,29)(26,30)(27,31)(32,42)(33,40)(34,41)(35,43)(36,44)(37,45)(38,46)(39,48)(47,52)(49,51)(50,53);(14,16,17,21)(15,18,19,20)(22,24)(23,28)(25,32)(26,33)(27,34)(29,42)(30,40)(31,41)(35,47)(36,48)(37,49)(38,50)(39,44)(43,52)(45,51)(46,53);(22,25,27,36)(23,29,31,44)(24,32,34,48)(26,37,38,35)(28,39,41,42)(30,45,46,43)(33,49,50,47)(40,52,53,51);(15,19)(18,20)(22,26,27,38)(23,30,31,46)(24,33,34,50)(25,35,36,37)(28,40,41,53)(29,43,44,45)(32,47,48,49)(39,51,42,52)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16977);