Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12744 |
| 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 | |
874 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)(14,15,19,26,21,25,20,42)(16,27,30,55,31,54,43,51)(17,32,34,50,35,23,41,49)(18,36,38,52,40,69,39,24)(22,37,46,61,45,70,47,29)(28,56,58,75,60,53,59,74)(33,64,66,63,67,68,71,48)(44,65,72,57,62,76,73,77);(14,16)(15,22)(17,28)(18,37)(19,30)(20,43)(21,31)(23,44)(24,51)(25,45)(26,46)(27,36)(29,39)(32,62)(33,65)(34,58)(35,60)(38,61)(40,70)(41,59)(42,47)(48,74)(49,72)(50,73)(52,55)(53,68)(54,69)(56,64)(57,66)(63,75)(67,76)(71,77);(14,17,21,35)(15,23,25,32)(16,28,31,60)(18,33,40,67)(19,41,20,34)(22,44,45,62)(24,48,52,63)(26,50,42,49)(27,53,54,56)(29,57,61,77)(30,59,43,58)(36,68,69,64)(37,65,70,76)(38,71,39,66)(46,73,47,72)(51,74,55,75)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5732);