Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3584 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1084 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,21,27)(16,28,32,56)(17,33,37,48)(18,26,20,24)(19,39,42,51)(22,44,47,31)(23,34,50,36)(25,38,53,41)(29,57,61,75)(30,62,43,52)(35,66,69,49)(40,54,70,46)(45,67,73,77)(55,58,76,60)(59,63,71,72)(64,65,74,68);(14,16)(15,22)(17,29)(18,30)(19,40)(20,43)(21,32)(23,45)(24,46)(25,52)(26,54)(27,47)(28,39)(31,41)(33,63)(34,58)(35,67)(36,60)(37,61)(38,44)(42,70)(48,72)(49,75)(50,73)(51,56)(53,62)(55,64)(57,66)(59,68)(65,71)(69,77)(74,76);(14,17)(15,23)(16,29)(18,34)(19,35)(20,36)(21,37)(22,45)(24,48)(25,49)(26,33)(27,50)(28,55)(30,58)(31,59)(32,61)(38,65)(39,64)(40,67)(41,68)(42,69)(43,60)(44,71)(46,72)(47,73)(51,74)(52,75)(53,66)(54,63)(56,76)(57,62)(70,77);(14,18,21,20)(15,24,27,26)(16,30,32,43)(17,34,37,36)(19,38,42,41)(22,46,47,54)(23,48,50,33)(25,51,53,39)(28,52,56,62)(29,58,61,60)(31,40,44,70)(35,65,69,68)(45,72,73,63)(49,74,66,64)(55,75,76,57)(59,67,71,77)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26530);