Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,21,17,27)(16,23,26,28,25,29,24,20)(30,31,34,36,35,39,33,38)(32,40,42,37,43,44,41,45);(14,16)(15,20,21,28)(17,24)(18,26)(19,25)(22,23,27,29)(31,36)(33,34)(37,40)(38,39)(41,42)(44,45);(15,21)(17,18)(20,28)(24,26)(30,32,35,43)(31,37,39,45)(33,42,34,41)(36,40,38,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2285);