Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60388 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C210 |
| direct product | C13×#60389 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ G | |
4770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23)(16,24,27,37)(17,21,28,35)(18,30,32,22)(20,31,34,26)(25,38,39,45)(29,42,41,36)(33,43,44,40);(14,16)(15,20)(17,25)(18,31)(19,27)(21,33)(22,37)(23,34)(24,30)(26,32)(28,39)(29,43)(35,44)(36,45)(38,42)(40,41);(18,32)(22,30)(24,37)(26,31)(29,41)(36,42)(38,45)(40,43);(14,17)(15,21)(16,25)(18,29)(19,28)(20,33)(22,36)(23,35)(24,38)(26,40)(27,39)(30,42)(31,43)(32,41)(34,44)(37,45);(17,28)(21,35)(25,39)(29,41)(33,44)(36,42)(38,45)(40,43)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53377);