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AGL(1,𝔽7)×C23⋊C11 #24922327

order10626
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽7)×C23⋊C11
unambiguous semidirect productD7⋊(C3×C23⋊C11)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C23⋊C11)
unambiguous semidirect product(C23×AGL(1,𝔽7))⋊C11
unambiguous semidirect product(D7×C23⋊C11)⋊C3

Splittings

Fitting, socle, derived, HallC7×C23 ⋊ C2×C3×C11
HallΓL(1,𝔽8)×C23⋊C11 ⋊ C2
HallD7×C23⋊C11 ⋊ C3
HallC7×C23⋊C11 ⋊ C2×C3
HallC23×AGL(1,𝔽7) ⋊ C11
HallΓL(1,𝔽8)×C23 ⋊ C2×C11
HallD7×C23 ⋊ C3×C11
SylowC23 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C23⋊C11
HallD7 ⋊ C3×C23⋊C11
SylowC7 ⋊ C2×C3×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C23C2×C3×C11
LCSG ▷ C7×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×AGL(1,𝔽23), C2×AGL(1,𝔽7)×C23⋊C11, C3×AGL(1,𝔽7)×C23⋊C11, …
maximal normal subgroup ofAGL(1,𝔽7)×AGL(1,𝔽23), C2×AGL(1,𝔽7)×C23⋊C11, C3×AGL(1,𝔽7)×C23⋊C11
maximal quotient ofΓL(1,𝔽8)⋊C4×C23⋊C11, C2×AGL(1,𝔽7)×C23⋊C11, D7⋊C9×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 35);