Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#29387 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2598 |
| prime radical | C13×#2017 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
646 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)(16,26)(17,30)(18,23)(19,24)(20,25)(21,28)(22,32)(27,35)(29,36)(31,40)(33,37)(34,39)(38,42)(41,44)(43,45);(14,16,18,28,20,29,19,33)(15,21,24,26,25,37,23,36)(17,27,32,43,31,42,34,44)(22,38,30,45,39,35,40,41);(14,17)(15,22)(16,27)(18,32)(19,34)(20,31)(21,35)(23,40)(24,30)(25,39)(26,41)(28,43)(29,42)(33,44)(36,45)(37,38);(15,23,25,24)(17,31)(21,36,37,26)(22,30,39,40)(27,42)(32,34)(35,41,38,45)(43,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22375);