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C5×ΓL(1,𝔽8)×D35 #20301270

order7350
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D35
unambiguous semidirect productC5⋊(C5×D7×ΓL(1,𝔽8))

Splittings

Fitting, socle, HallC52×C72 ⋊ C2×C3
derivedC5×C72 ⋊ C2×C3×C5
HallC52×C7×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×D35 ⋊ C3
HallC7×ΓL(1,𝔽8) ⋊ C5×D5
SylowC72 ⋊ C3×C5×D5
SylowC52 ⋊ D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D35
commutator, hypocenterC5×C72C2×C3×C5
FrattiniC1G
Fitting, socleC52×C72C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C5

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D35, C5×(C5⋊AGL(1,𝔽7))⋊D7, C5×D5×D7×ΓL(1,𝔽8), …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D35, C5×(C5⋊AGL(1,𝔽7))⋊D7, C5×D5×D7×ΓL(1,𝔽8), …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic35, C2×C5×ΓL(1,𝔽8)×D35, C5×C7⋊C9×D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 93);