Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#3068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
466 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)(15,19)(16,22)(17,25)(21,27)(23,24)(26,29);(14,15,17,19,18,21,25,27)(16,20,23,26,24,28,22,29);(14,16)(15,20)(17,23)(18,24)(19,26)(21,28)(22,25)(27,29);(15,21)(19,27)(20,28)(26,29)377 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1800);