Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1146 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)(14,15)(16,24)(17,21)(18,31)(19,23)(20,28)(22,34)(25,32)(26,42)(27,38)(29,39)(30,37)(33,36)(35,44)(40,43)(41,45);(14,15)(16,25,27,20)(17,21)(18,22)(19,23)(24,28,38,32)(26,41,43,35)(29,36)(30,37)(31,34)(33,39)(40,45,42,44);(14,16)(15,20)(17,26)(18,32)(19,27)(21,35)(22,38)(23,25)(24,31)(28,34)(29,45)(30,43)(33,44)(36,40)(37,41)(39,42);(14,17,19,30)(15,21,23,37)(16,26,27,43)(18,33,34,29)(20,35,25,41)(22,39,31,36)(24,40,38,42)(28,45,32,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16987);