Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61057 |
| 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×#525 ◁ G | |
2696 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)(14,15)(16,17)(18,19,24,29)(20,30,33,44)(21,26,36,43)(22,28,23,27)(25,37,40,32)(31,46,48,41)(34,49,47,39)(35,45,38,42);(18,20,24,33)(19,25,29,40)(21,34,36,47)(22,32,23,37)(26,41,43,46)(27,30,28,44)(31,38,48,35)(39,45,49,42);(15,17);(18,21)(19,26)(20,31)(22,35)(23,38)(24,36)(25,39)(27,42)(28,45)(29,43)(30,46)(32,47)(33,48)(34,37)(40,49)(41,44);(18,22,24,23)(19,27,29,28)(20,32,33,37)(21,35,36,38)(25,30,40,44)(26,42,43,45)(31,47,48,34)(39,46,49,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54045);