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×#24295 |
| 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 | |
1302 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)(16,18)(17,30)(19,38)(20,25)(21,26)(22,28)(23,34)(24,36)(27,39)(29,37)(31,32)(33,41)(35,40)(42,45)(43,44);(14,16,19,28,21,29,20,24)(15,22,25,18,26,36,38,37)(17,31,33,27,35,42,34,43)(23,32,40,44,41,45,30,39);(14,17)(15,23)(16,27)(18,32)(19,33)(20,34)(21,35)(22,39)(24,31)(25,40)(26,41)(28,42)(29,43)(30,38)(36,44)(37,45);(14,18,19,36,21,37,20,22)(15,24,25,16,26,28,38,29)(17,32,33,44,35,45,34,39)(23,31,40,27,41,42,30,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17283);