Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60627 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1998 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)(16,19)(17,18)(20,21)(22,23,29,35)(24,31,38,44)(25,30,37,45)(26,32,40,47)(27,34,28,33)(36,46,50,53)(39,43,51,52)(41,49,42,48);(15,18)(19,21)(22,24,27,25,29,38,28,37)(23,30,33,31,35,45,34,44)(26,36,41,39,40,50,42,51)(32,43,48,46,47,52,49,53);(14,16,17,20)(15,19,18,21)(22,25,27,38,29,37,28,24)(23,31,33,45,35,44,34,30)(26,39,41,50,40,51,42,36)(32,46,48,52,47,53,49,43);(22,26)(23,32)(24,36)(25,39)(27,41)(28,42)(29,40)(30,43)(31,46)(33,48)(34,49)(35,47)(37,51)(38,50)(44,53)(45,52);(26,40)(32,47)(36,50)(39,51)(41,42)(43,52)(46,53)(48,49)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53615);