Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#3585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C25×C13 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ G | |
1464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,25)(23,27)(24,26)(28,29);(15,19)(17,25)(20,26)(21,22)(24,29)(27,28);(14,16)(15,20)(17,24)(18,23)(19,26)(21,27)(22,28)(25,29);(16,23)(20,27)(24,29)(26,28);(15,21)(19,22)(20,27)(26,28)533 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2317);