Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C3×C4 |
| Hall | C7×Dic133 ⋊ C3 |
| Hall | C7×#87705 ⋊ C4 |
| Sylow | C72 ⋊ (C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19150318 |
| commutator, hypocenter | C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C19 | C2×C3 |
| prime radical | C2×C7×#87705 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,19,2|a^2=f,d^a=d^6,e^a=e^18,c^b=c^2,e^b=e^11344 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#13097583, #45691758, #45691761, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#13097583, #45691758, #45691761, … |
| maximal quotient of | #45691510, C3×#26013851, C3⋊#26013851 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 113);