Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1874 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
476 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)(14,15,20,27,21,28,45,59,22,29,44,58,19,26,18,25)(16,30,34,52,35,56,32,49,36,63,42,23,33,50,70,51)(17,37,40,57,39,55,43,61,41,60,47,53,46,24,38,54)(31,64,67,75,66,74,65,76,68,77,72,73,71,62,69,48);(14,16,21,33,22,36,19,35)(15,23,28,49,29,52,26,51)(17,31,39,71,41,68,46,66)(18,42,20,32,45,34,44,70)(24,48,37,73,55,76,60,75)(25,56,27,30,59,50,58,63)(38,72,40,65,43,67,47,69)(53,77,54,74,57,64,61,62);(14,17)(15,24)(16,31)(18,43)(19,46)(20,47)(21,39)(22,41)(23,48)(25,57)(26,60)(27,61)(28,37)(29,55)(30,62)(32,69)(33,71)(34,72)(35,66)(36,68)(38,45)(40,44)(42,67)(49,73)(50,77)(51,75)(52,76)(53,59)(54,58)(56,64)(63,74)(65,70)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5983);