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AGL(1,𝔽7)×#1043 #72218909

order4200
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽7)×#1043

Splittings

Fitting, socle, derived, HallC52×C7 ⋊ C2×C3×C4
HallD7×#1043 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C2×C4
SylowC52 ⋊ C4×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×#1043
SylowC7 ⋊ C2×C3×#1043

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C7C2×C3×C4
prime radicalAGL(1,𝔽7)×C5⋊D5C2
cosocleC7×C5⋊D5C22×C3
LCSG ▷ C52×C7
UCSC1

256 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D5⋊AGL(1,𝔽5), #1043×#64424, C2×AGL(1,𝔽7)×#1043, …
maximal normal subgroup ofAGL(1,𝔽7)×D5⋊AGL(1,𝔽5), C2×AGL(1,𝔽7)×#1043, C3×AGL(1,𝔽7)×#1043
maximal quotient of#1043×#64424, C2×AGL(1,𝔽7)×#1043, C3×AGL(1,𝔽7)×#1043, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.