Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12827 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1804 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
376 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)(16,27,31,46)(17,32)(18,23)(19,39)(20,26)(21,29,45,62)(22,34)(24,37)(25,38)(28,56,59,77)(30,44,40,51)(33,65)(35,66)(36,52)(41,47)(42,50)(43,72,75,63)(48,70)(49,69)(53,68)(54,67,73,58)(55,71,76,61)(57,74,60,64);(14,16,20,31)(15,21)(17,28,35,59)(18,29,38,62)(19,40,42,30)(22,43)(23,27)(24,51)(25,46)(26,45)(32,64)(33,57,36,60)(34,67,69,58)(37,71,68,61)(39,55)(41,72,70,63)(44,53)(47,73)(48,54)(49,75)(50,76)(52,77)(56,65)(66,74);(14,17,20,35)(15,22,26,49)(16,28,31,59)(18,36,38,33)(19,41,42,70)(21,43,45,75)(23,48,25,47)(24,52,53,65)(27,54,46,73)(29,60,62,57)(30,63,40,72)(32,50,66,39)(34,68,69,37)(44,56,51,77)(55,64,76,74)(58,71,67,61)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5815);