Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12750 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12751 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1786 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#578 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
876 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)(16,27,31,55)(17,33,36,51)(18,38)(19,24)(20,26)(21,29,45,61)(22,35,47,37)(23,40)(25,42)(28,56)(30,54,32,48)(34,66,69,46)(39,52,62,44)(41,49)(43,71)(50,60)(53,63)(57,72)(58,76)(59,75)(64,77)(65,68,74,70)(67,73);(14,16)(15,21)(17,28)(18,39)(19,30)(20,31)(22,43)(23,48)(24,44)(25,52)(26,45)(27,49)(29,60)(32,42)(33,64)(34,67)(35,58)(36,59)(37,63)(38,55)(40,61)(41,62)(46,56)(47,73)(50,54)(51,72)(53,74)(57,68)(65,76)(66,75)(69,71)(70,77);(14,17,20,36)(15,22,26,47)(16,28,31,59)(18,34,41,69)(19,37,42,35)(21,43,45,73)(23,46,50,66)(24,51,25,33)(27,53,55,76)(29,57,61,77)(30,63,32,58)(38,65,49,74)(39,67,62,71)(40,70,60,68)(44,72,52,64)(48,56,54,75)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5739);