Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12915 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #120 |
| commutator | C23 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1850 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,19,24,33,43,20,25,34,44,35,45,56,66)(16,21,28,38,29,39,52,62,27,37,50,60,51,61,71,75)(17,22,31,41,32,42,55,65,30,40,53,63,54,64,72,76)(26,46,48,67,49,68,70,77,47,36,57,58,69,59,73,74);(14,16,18,28,19,29,33,52,20,27,34,50,35,51,56,71)(15,21,23,38,24,39,43,62,25,37,44,60,45,61,66,75)(17,26,31,48,32,49,55,70,30,47,53,57,54,69,72,73)(22,36,41,58,42,59,65,74,40,46,63,67,64,68,76,77);(14,17)(15,22)(16,26)(18,31)(19,32)(20,30)(21,36)(23,41)(24,42)(25,40)(27,47)(28,48)(29,49)(33,55)(34,53)(35,54)(37,46)(38,58)(39,59)(43,65)(44,63)(45,64)(50,57)(51,69)(52,70)(56,72)(60,67)(61,68)(62,74)(66,76)(71,73)(75,77)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5903);