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×#29385 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2598 |
| prime radical | C13×#2010 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
662 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)(16,25)(17,21)(18,22)(19,24)(20,27)(23,31)(26,40)(28,33)(29,37)(30,38)(32,45)(34,43)(35,42)(36,44)(39,41);(14,16,18,27,19,28,31,43)(15,20,23,25,24,34,22,33)(17,26,30,42,29,41,44,45)(21,35,36,40,37,32,38,39);(14,17)(15,21)(16,26)(18,30)(19,29)(20,32)(22,38)(23,36)(24,37)(25,39)(27,42)(28,41)(31,44)(33,40)(34,35)(43,45);(15,22,24,23)(17,29)(20,33,34,25)(21,36,37,38)(26,41)(30,44)(32,39,35,40)(42,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22373);