Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28×C4 |
| direct product | C13×#60651 |
| 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 ◁ C4×C13×#41 ◁ G | |
3138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,23,27)(20,28,29,41)(21,25,32,39)(22,34,35,26)(24,36,37,31)(30,42,43,49)(33,46,45,40)(38,47,48,44);(18,20,22,31,23,29,35,36)(19,24,26,28,27,37,34,41)(21,30,33,44,32,43,45,47)(25,38,40,42,39,48,46,49);(14,15,16,17)(20,29)(24,37)(28,41)(30,43)(31,36)(38,48)(42,49)(44,47);(18,21)(19,25)(20,30)(22,33)(23,32)(24,38)(26,40)(27,39)(28,42)(29,43)(31,44)(34,46)(35,45)(36,47)(37,48)(41,49);(21,32)(25,39)(30,43)(33,45)(38,48)(40,46)(42,49)(44,47)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53639);