Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C13 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ G | |
5992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 6 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,24)(18,19)(21,25)(22,26)(23,29)(27,28);(15,19)(20,26)(21,24)(27,29);(16,22)(20,26)(23,28)(27,29);(14,16)(15,20)(17,23)(18,22)(19,26)(21,27)(24,29)(25,28);(14,15)(16,20)(17,21)(18,19)(22,26)(23,27)(24,25)(28,29);(14,17)(15,21)(16,23)(18,25)(19,24)(20,27)(22,28)(26,29)845 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2326);