Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#3288 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(17,18)(21,28)(22,26)(23,29)(24,27);(14,15)(16,23)(17,26)(18,20)(19,22)(21,24)(25,28)(27,29);(14,15)(16,21)(17,20)(18,26)(19,22)(23,24)(25,29)(27,28);(14,16)(15,21)(17,27)(18,24)(19,25)(20,28)(22,29)(23,26)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2020);