Finite Group DatabasebetaFinite Group Databasebeta| order | 2310 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D55 |
| unambiguous semidirect product | C5⋊(ΓL(1,𝔽8)×D11) |
| unambiguous semidirect product | C11⋊(D5×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D55)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C11 | C2×C3 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 385 |
A minimal faithful permutation representation — 2 generators on 23 points:
(2,3,4)(5,7,6)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23);(1,2,3,5,4,6,7)(9,12)(10,11)(14,23)(15,22)(16,21)(17,20)(18,19)145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2310, 31);