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×#17601 |
| 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×#121 | C23 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×Q8×C13 ◁ G | |
882 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)(32,39)(33,36)(34,38)(35,43)(37,41)(40,44)(42,45);(14,16)(15,19)(17,25)(18,24)(20,27)(21,29)(22,28)(23,26)(30,32)(31,37)(33,40)(34,41)(35,44)(36,42)(38,45)(39,43);(15,20)(19,27)(21,28)(22,29)(30,33,36,31)(32,40,42,37)(34,38,35,43)(39,41,45,44);(30,34,36,35)(31,38,33,43)(32,41,42,44)(37,45,40,39)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10589);