Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3499 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1178 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)(22,23,28,32)(24,29,35,46)(25,36,38,49)(26,40,27,31)(30,42,48,39)(33,47,50,53)(34,45,41,44)(37,52,51,43);(14,16,18,17)(15,19,21,20)(22,24)(23,29)(25,37)(26,34)(27,41)(28,35)(30,47)(31,44)(32,46)(33,39)(36,52)(38,51)(40,45)(42,50)(43,49)(48,53);(14,16,18,17)(15,20,21,19)(22,25,26,39,28,38,27,42)(23,30,31,36,32,48,40,49)(24,33,34,51,35,50,41,37)(29,43,44,47,46,52,45,53);(14,17,18,16)(15,20,21,19)(25,38)(30,48)(33,50)(36,49)(37,51)(39,42)(43,52)(47,53)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18867);