Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61668 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2200 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,23)(24,29)(25,31)(26,32)(27,36)(28,33)(30,34)(35,37);(14,16)(15,18)(17,21)(19,20)(22,24,28,25)(23,29,33,31)(26,35,27,34)(30,32,37,36);(22,24,28,25)(23,30,33,37)(26,34,27,35)(29,32,31,36);(16,21)(18,20)(22,25,28,24)(23,31,33,29)(26,34,27,35)(30,36,37,32);(15,19)(18,20)(22,26,28,27)(23,32,33,36)(24,34,25,35)(29,30,31,37)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54656);