Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,25)(18,21)(23,33)(24,34)(26,41)(27,28)(29,30)(32,36)(35,44)(38,39)(40,42);(14,15,21,34,19,24,18,20)(16,22,25,36,28,37,27,32)(17,23,30,38,31,39,29,33)(26,35,40,45,42,44,41,43);(14,16)(15,22)(17,26)(18,27)(19,28)(20,32)(21,25)(23,35)(24,37)(29,41)(30,40)(31,42)(33,43)(34,36)(38,45)(39,44);(14,17)(15,23)(16,26)(18,29)(19,31)(20,33)(21,30)(22,35)(24,39)(25,40)(27,41)(28,42)(32,43)(34,38)(36,45)(37,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25939);