Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23×C42 |
| direct product | C13×#21812 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
1354 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)(14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27)(28,36)(29,35)(30,32)(31,34)(33,37)(38,41)(39,40);(18,20,21,25)(19,22,23,24)(27,32)(33,40)(34,35)(36,41);(20,25)(22,24)(26,28)(27,33)(29,37)(30,38)(31,39)(32,40)(34,36)(35,41);(19,23)(22,24)(26,29,30,31)(27,34,32,35)(28,37,38,39)(33,36,40,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14800);