Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G | |
1824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(22,23)(24,29)(25,34)(26,30)(27,35)(28,31)(32,36)(33,37);(15,17)(18,19)(20,21)(22,24,28,33)(23,29,31,37)(25,27,32,26)(30,34,35,36);(19,21)(22,25)(23,29)(24,26)(27,33)(28,32)(30,36)(31,37)(34,35);(15,17)(22,26,28,27)(23,30,31,35)(24,32,33,25)(29,36,37,34)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16917);