Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
658 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)(14,15,16,17)(19,24)(21,25)(22,32)(26,34)(27,42)(28,37)(30,38)(31,44)(33,39)(35,36)(40,45)(41,49)(43,48)(46,47);(18,19,25,36,22,27,33,37,23,28,39,42,32,35,21,24)(20,26,38,47,31,41,43,45,29,40,48,49,44,46,30,34);(18,20)(19,26)(21,30)(22,31)(23,29)(24,34)(25,38)(27,41)(28,40)(32,44)(33,43)(35,46)(36,47)(37,45)(39,48)(42,49);(20,29)(26,40)(30,43)(31,44)(34,45)(38,48)(41,46)(47,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26398);