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ΓL(1,𝔽8)×C5⋊D35 #20301281

order7350
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productΓL(1,𝔽8)×C5⋊D35
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D35)

Splittings

Fitting, socle, derived, HallC52×C72 ⋊ C2×C3
HallC52×C7×ΓL(1,𝔽8) ⋊ C2
HallC7×C5⋊D35 ⋊ C3
HallC7×ΓL(1,𝔽8) ⋊ C5⋊D5
SylowC72 ⋊ C3×C5⋊D5
SylowC52 ⋊ D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C72C2×C3
LCSG ▷ C52×C72
UCSC1

136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

445 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C5⋊D35, (ΓL(1,𝔽8)⋊D7)⋊(C5⋊D5), D7×ΓL(1,𝔽8)×C5⋊D5, …
maximal normal subgroup ofAGL(1,𝔽7)×C5⋊D35, (ΓL(1,𝔽8)⋊D7)⋊(C5⋊D5), D7×ΓL(1,𝔽8)×C5⋊D5, …
maximal quotient ofΓL(1,𝔽8)×C7⋊#1039, C2×ΓL(1,𝔽8)×C5⋊D35, C7⋊C9×C5⋊D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 104);