Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#121 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
412 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,23,17,21)(16,24,26,20,27,28,25,29)(30,31,34,38,35,37,44,32)(33,40,42,45,41,36,43,39);(14,16)(15,20)(17,26)(18,25)(19,27)(21,28)(22,24)(23,29)(30,32,34,37,35,38,44,31)(33,39,43,40,41,45,42,36);(14,16)(15,20)(17,25)(18,26)(19,27)(21,24)(22,28)(23,29)(30,33)(31,36)(32,39)(34,43)(35,41)(37,40)(38,45)(42,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2325);