Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
528 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)(14,15,20,24,19,25,37,45)(16,21,29,41,28,40,38,43)(17,30,33,34,32,22,42,27)(18,23,36,26,35,31,39,44);(14,16)(15,21)(17,31)(18,34)(19,28)(20,38)(22,39)(23,32)(24,43)(25,40)(26,33)(27,35)(29,37)(30,36)(41,45)(42,44);(14,17,19,32)(15,22)(16,26)(18,21,35,40)(20,33,37,42)(23,38)(24,27)(25,30)(28,44)(29,31)(34,45)(36,41,39,43);(14,18,19,35)(15,23,25,31)(16,27,28,34)(17,21,32,40)(20,39,37,36)(22,38,30,29)(24,44,45,26)(33,43,42,41)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25685);