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C2×C5×ΓL(1,𝔽8)×C43 #22583271

order9030
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C43
unambiguous semidirect product(C2×C7)⋊(C3×C5×C43)
unambiguous semidirect product(C2×C5×C7)⋊(C3×C43)

Splittings

Fitting, socle, HallC2×C5×C7×C43 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C5×C43
HallC5×C7×C43 ⋊ C2×C3
HallC2×C7×C43 ⋊ C3×C5
HallC7×C43 ⋊ C2×C3×C5
HallC2×C5×C7 ⋊ C3×C43
HallC5×C7 ⋊ C2×C3×C43
HallC2×C7 ⋊ C3×C5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C5×C43ΓL(1,𝔽8)
commutator, hypocenterC7C2×C3×C5×C43
FrattiniC1G
Fitting, socleC2×C5×C7×C43C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×ΓL(1,𝔽8)×C43, C5×ΓL(1,𝔽8)×Dic43, C5×C43×ΓL(1,𝔽8)⋊C4, …
maximal normal subgroup ofC4×C5×ΓL(1,𝔽8)×C43, C5×ΓL(1,𝔽8)×Dic43, C5×C43×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofC4×C5×ΓL(1,𝔽8)×C43, C22×C5×ΓL(1,𝔽8)×C43, C2×C5×C43×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 4);