Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2018 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
502 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)(14,15,18,22,20,25,19,24)(16,26,29,21,30,36,27,37)(17,23,33,38,34,39,32,40)(28,41,43,35,31,44,42,45);(14,16,18,29,20,30,19,27)(15,21,24,26,25,37,22,36)(17,31,32,43,34,28,33,42)(23,35,38,44,39,45,40,41);(15,22)(16,27)(17,32)(18,19)(23,39)(24,25)(26,36)(28,31)(29,30)(33,34)(35,44)(41,45);(14,17)(15,23)(16,28)(18,33)(19,32)(20,34)(21,35)(22,38)(24,40)(25,39)(26,41)(27,42)(29,43)(30,31)(36,44)(37,45)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25858);