Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#21784 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24,27,20)(17,28,30,40)(18,23)(19,22)(21,29,37,32)(25,41)(26,39,31,35)(33,38)(34,42)(36,44)(43,45);(14,16)(15,20)(17,25)(18,31)(19,27)(21,36)(22,24)(23,39)(26,33)(28,45)(29,44)(30,43)(32,42)(34,37)(35,38)(40,41);(14,17,19,30)(15,21,22,37)(16,25,27,43)(18,32,33,29)(20,34,24,36)(23,40,38,28)(26,44,31,42)(35,41,39,45);(14,16)(15,20)(17,25)(18,26)(19,27)(21,34)(22,24)(23,35)(28,45)(29,42)(30,43)(31,33)(32,44)(36,37)(38,39)(40,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14772);