Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D105 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×D35) |
| unambiguous semidirect product | C5⋊(ΓL(1,𝔽8)×D21) |
| Fitting, socle, derived | C3×C5×C72 ⋊ C2×C3 |
| Hall | C3×C5×C7×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ D5 |
| Hall | C5×C72 ⋊ C3×D3 |
| Sylow | C72 ⋊ C3×D15 |
| Sylow | C5 ⋊ ΓL(1,𝔽8)×D21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C72 | C2×C3 |
| LCS | G ▷ C3×C5×C72 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 630 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)×D525, C5×ΓL(1,𝔽8)×D105, ΓL(1,𝔽8)×C3⋊(C5⋊D35) |
| maximal normal subgroup of | C5×ΓL(1,𝔽8)×D105 |
| maximal quotient of | ΓL(1,𝔽8)×D525, C5×ΓL(1,𝔽8)×D105, ΓL(1,𝔽8)×C3⋊(C5⋊D35) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 115);