Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C112 ⋊ C3×C4 |
| Hall | C7⋊#92150 ⋊ C3 |
| Hall | C7⋊(C112⋊C3) ⋊ C4 |
| Sylow | C112 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ #92150⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C112 | C3×C4 |
| prime radical | (C11⋊D11)⋊ΓL(1,𝔽8) | C2 |
| cosocle | C7×C11⋊D11 | C2×C3 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7,11^2|a^2=c,d^a=d^6,e^a=e^10f^7,f^a=e^6f,d^b=d^2,e^b=e^2f^10,f^b=e^7f^8,e^c=e^10,f^c=f^1084 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊(#92150⋊C3), C3×#23779019, C3⋊#23779019 |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(#92150⋊C3), C3×#23779019 |
| maximal quotient of | #44478925, C3×#23779019, C3⋊#23779019 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 71);