Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#18260 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,21)(22,23)(24,34)(25,30)(26,32)(27,31)(28,33)(29,35)(36,37);(14,15)(16,18)(17,19)(20,21)(22,24,28,25)(23,29,33,37)(26,35,27,36)(30,31,34,32);(14,16)(15,18)(17,20)(19,21)(22,25,28,24)(23,30,33,34)(26,35,27,36)(29,31,37,32);(22,26,28,27)(23,31,33,32)(24,35,25,36)(29,34,37,30)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11248);