Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24772 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19,22,27,24,29,23,28)(20,25,31,40,32,41,38,45)(21,33,35,44,37,43,36,26)(30,42,34,48,46,49,47,39);(14,15,17,16)(18,20)(19,25)(21,34)(22,31)(23,38)(24,32)(26,42)(27,40)(28,45)(29,41)(30,36)(33,48)(35,46)(37,47)(39,43)(44,49);(18,21,24,37)(19,26,29,44)(20,30,32,46)(22,36,23,35)(25,39,41,48)(27,43,28,33)(31,47,38,34)(40,49,45,42);(14,16,17,15)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17760);