Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C2×C43 |
| direct product | C13×#14617 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(19,22)(20,24)(26,27,29,30)(28,31,32,33);(19,22)(23,25)(27,30)(28,32)(34,35,37,39)(36,38,40,41);(14,16,17,15)(18,19)(20,23)(21,22)(24,25)(26,27)(28,31)(29,30)(32,33)(34,35)(36,38)(37,39)(40,41);(18,20)(19,23)(21,24)(22,25)(26,28,29,32)(27,31,30,33)(34,36,37,40)(35,38,39,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 7605);