Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#14584116 |
| Fitting, socle, Hall | C22×C72×C19 ⋊ C3 |
| derived, Hall | C72×C19 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C19⋊C3 |
| Hall | C22×C19 ⋊ #3861 |
| Sylow | C72 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C22×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14584116 |
| commutator, cosocle, hypocenter | C72×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C22 | |
200 conjugacy classes of subgroups.
1252 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45692509, #45692511, A4×#14584116, … |
| maximal normal subgroup of | #45692509, #45692511, A4×#14584116, … |
| maximal quotient of | C22×#22552710, C2×D3×#14584116, C22×C3×#14584116 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 306);