Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24420 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1326 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)(14,15,18,24,20,21,19,25)(16,26,30,35,29,37,27,22)(17,31,32,39,33,23,34,38)(28,40,41,36,42,45,43,44);(15,21)(16,27)(18,19)(22,26)(23,31)(28,41)(29,30)(32,34)(35,37)(36,40)(42,43)(44,45);(14,16)(15,22)(17,28)(18,27)(19,30)(20,29)(21,35)(23,36)(24,37)(25,26)(31,44)(32,43)(33,42)(34,41)(38,40)(39,45);(14,17)(15,23)(16,28)(18,34)(19,32)(20,33)(21,31)(22,36)(24,39)(25,38)(26,40)(27,41)(29,42)(30,43)(35,44)(37,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17408);