Finite Group DatabasebetaFinite Group Databasebeta| order | 9156 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C109 ⋊ C3×C4 |
| Hall | Dic763 ⋊ C3 |
| Hall | #14556233 ⋊ C4 |
| Sylow | C109 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ Dic109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #17987087 |
| commutator, hypocenter | C7×C109 | C3×C4 |
| Fitting, socle | C2×C7×C109 | C2×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,109,2|a^2=e,c^a=c^6,d^a=d^108,c^b=c^2,d^b=d^45266 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊(Dic109⋊C3), C3×#22603880, C3⋊#22603880 |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(Dic109⋊C3), C3×#22603880 |
| maximal quotient of | #42117343, C3×#22603880, C3⋊#22603880 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9156, 24);