Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60753 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60809 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#117 ◁ G | |
2034 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 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)(22,23,28,33)(24,29,35,43)(25,38,40,47)(26,32,27,31)(30,41,46,39)(34,48,49,53)(36,45,37,44)(42,51,52,50);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,34)(26,36)(27,37)(28,35)(30,42)(31,44)(32,45)(33,43)(38,48)(39,50)(40,49)(41,51)(46,52)(47,53);(16,21)(18,20)(22,25)(23,30)(24,34)(26,39)(27,41)(28,40)(29,42)(31,38)(32,47)(33,46)(35,49)(36,50)(37,51)(43,52)(44,48)(45,53);(15,19)(18,20)(24,35)(29,43)(34,49)(36,37)(42,52)(44,45)(48,53)(50,51);(22,26,28,27)(23,31,33,32)(24,36,35,37)(25,39,40,41)(29,44,43,45)(30,38,46,47)(34,50,49,51)(42,48,52,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53797);