Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1334 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)(14,15,21,24)(16,19,27,20)(17,28,32,25)(18,26,35,40)(22,30,37,31)(23,34,38,33)(29,36,44,45)(39,42,41,43);(14,16,19,24,21,27,20,15)(17,22,30,25,32,37,31,28)(18,26,33,38,35,40,34,23)(29,36,42,39,44,45,43,41);(14,17)(15,22)(16,25)(18,29)(19,30)(20,31)(21,32)(23,36)(24,37)(26,39)(27,28)(33,42)(34,43)(35,44)(38,45)(40,41);(14,18,20,34,21,35,19,33)(15,23,27,40,24,38,16,26)(17,29,31,43,32,44,30,42)(22,36,28,41,37,45,25,39)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17285);