Finite Group DatabasebetaFinite Group Databasebeta| order | 18669 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#14581887 |
| Fitting, socle, Hall | C72×C127 ⋊ C3 |
| derived | C7×C127 ⋊ C3×C7 |
| Sylow | C127 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #14581887 |
| commutator, cosocle, hypocenter | C7×C127 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C127 | C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2667 |
2093 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#19128625, C7×#19128633, C7×#19128629, … |
| maximal normal subgroup of | C7×#19128625, C7×#19128633, C7×#19128629, … |
| maximal quotient of | C2×C7×#14581887 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18669, 17);