Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #2263 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#2264 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C23×C13 |
| prime radical | C13×#508 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ C2×C13×C16 ◁ G | |
104 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)(16,26)(17,31)(18,37)(19,41)(20,22)(21,27)(23,34)(24,33)(25,39)(28,58)(29,61)(30,53)(32,50)(35,69)(36,52)(38,48)(40,71)(42,54)(43,57)(44,65)(45,64)(46,55)(47,59)(49,76)(51,56)(60,77)(62,67)(63,68)(66,75)(70,73)(72,74);(14,16,20,30)(15,21,22,43)(17,32,36,66)(18,38,40,72)(19,42,39,29)(23,48,46,74)(24,50,47,75)(25,51,41,45)(26,52,53,31)(27,55,57,34)(28,59,60,33)(35,70,68,65)(37,44,71,73)(49,77,62,58)(54,63,61,69)(56,67,64,76);(15,22)(21,43)(23,46)(24,47)(25,41)(26,53)(31,52)(37,71)(44,73)(45,51)(48,74)(49,62)(50,75)(54,61)(58,77)(63,69)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 996);