Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28×C4 |
| direct product | C13×#60649 |
| 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 | |
3178 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)(20,28)(21,26)(22,34)(23,25)(24,30)(27,35)(29,41)(31,40)(32,38)(33,46)(36,44)(37,43)(39,45)(42,48)(47,49);(18,20,22,30,23,31,35,44)(19,24,27,28,25,36,34,40)(21,29,33,43,32,42,45,49)(26,37,39,41,38,47,46,48);(14,15,16,17)(19,25)(24,36)(26,38)(27,34)(28,40)(37,47)(39,46)(41,48);(18,21)(19,26)(20,29)(22,33)(23,32)(24,37)(25,38)(27,39)(28,41)(30,43)(31,42)(34,46)(35,45)(36,47)(40,48)(44,49);(21,32)(26,38)(29,42)(33,45)(37,47)(39,46)(41,48)(43,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53637);