Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12917 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C2×D4 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C8×D4 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C22×C13×C16 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,30,25,29,42,47,22,28,38,31,23,39,41,48)(20,21,34,37,35,36,27,45,32,26,43,44,33,40,46,49);(15,17)(18,20,24,34,25,35,42,27,22,32,38,43,23,33,41,46)(19,26,30,44,29,40,47,49,28,21,31,37,39,36,48,45);(18,21)(19,27)(20,31)(22,26)(23,40)(24,37)(25,36)(28,46)(29,43)(30,32)(33,47)(34,39)(35,48)(38,44)(41,49)(42,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5905);