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 | C7×Dic109 ⋊ C3 |
| Hall | #14556234 ⋊ C4 |
| Hall | Dic109 ⋊ ΓL(1,𝔽8) |
| Sylow | C109 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ Dic109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #17987078 |
| 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,d^a=d^108,c^b=c^2,d^b=d^63272 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×Dic109⋊C3, C3×#22603871, C3⋊#22603871 |
| maximal normal subgroup of | ΓL(1,𝔽8)×Dic109⋊C3, C3×#22603871 |
| maximal quotient of | #42117334, C3×#22603871, C3⋊#22603871 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9156, 15);