Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17602 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3522 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×Q8×C13 ◁ G | |
938 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,22,24,29)(17,21)(18,20)(19,23,27,25)(26,28)(30,31)(32,38)(33,42)(34,39)(35,44)(36,40)(37,41)(43,45);(14,16)(15,19)(17,25)(18,24)(20,27)(21,29)(22,28)(23,26)(30,32,36,33)(31,37,40,45)(34,41,35,43)(38,39,42,44);(15,20)(19,27)(21,28)(22,29)(30,33,36,32)(31,38,40,42)(34,41,35,43)(37,39,45,44);(30,34,36,35)(31,39,40,44)(32,41,33,43)(37,42,45,38)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10590);