Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#1420 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #357 |
| commutator | C16 | C2×C4×C13 |
| Frattini, cosocle | C2×C16 | C22×C13 |
| prime radical | C22×C13 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ C2×C13×C16 ◁ G | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 2 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,24,21,26,20,44)(16,27,29,58,32,60,31,67)(17,33,36,68,39,70,38,75)(19,40,35,56,43,51,42,25)(22,45,46,28,48,62,54,64)(23,49,52,74,53,73,69,37)(30,65,61,50,66,77,41,59)(34,55,71,76,63,57,72,47);(14,16,21,32)(15,22,26,48)(17,34,39,63)(18,31,20,29)(19,41,43,61)(23,50,53,59)(24,54,44,46)(25,55,56,57)(27,33,60,70)(28,37,64,74)(30,35,66,42)(36,72,38,71)(40,47,51,76)(45,49,62,73)(52,65,69,77)(58,75,67,68)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 152);