Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
1774 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,17)(16,20,21,19)(22,23,28,34)(24,29,37,45)(25,31,39,47)(26,33,27,32)(30,41,46,38)(35,43,51,52)(36,48,40,44)(42,49,53,50);(14,16)(15,19)(17,20)(18,21)(22,24,28,37)(23,29,34,45)(25,35,39,51)(26,40,27,36)(30,42,46,53)(31,43,47,52)(32,48,33,44)(38,50,41,49);(14,17,18,15)(16,20,21,19)(22,25)(23,30)(24,35)(26,38)(27,41)(28,39)(29,42)(31,32)(33,47)(34,46)(36,49)(37,51)(40,50)(43,48)(44,52)(45,53);(16,21)(19,20)(22,25)(23,31)(24,35)(26,41)(27,38)(28,39)(29,43)(30,32)(33,46)(34,47)(36,50)(37,51)(40,49)(42,48)(44,53)(45,52);(22,26,28,27)(23,32,34,33)(24,36,37,40)(25,38,39,41)(29,44,45,48)(30,31,46,47)(35,49,51,50)(42,52,53,43)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54278);