Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| isoclinism | isoclinic class of #87705 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C22×C7×#87705 |
| Fitting, socle, Hall | C22×C72×C19 ⋊ C3 |
| derived | C7×C19 ⋊ C22×C3×C7 |
| Hall | C72×C19 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C19⋊C3 |
| Hall | C22×C19 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C22×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | #87705 |
| commutator, cosocle, hypocenter | C7×C19 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C19 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C22×C7 | |
100 conjugacy classes of subgroups.
1316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 304);