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C22×ΓL(1,𝔽8)×C127 #24922630

order10668
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C22×C3×C127 · Schur multiplier (H2) = C2

Aliases

direct productC22×ΓL(1,𝔽8)×C127

Splittings

Fitting, socle, HallC22×C7×C127 ⋊ C3
derived, SylowC7 ⋊ C22×C3×C127
HallC7×C127 ⋊ C22×C3
HallC22×C7 ⋊ C3×C127

Subgroups

subgroupG/H
center, hypercenterC22×C127ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C22×C3×C127
FrattiniC1G
Fitting, socleC22×C7×C127C3
LCSG ▷ C7
UCSC1 ◁ C22×C127

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2540 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×ΓL(1,𝔽8)×C127, ΓL(1,𝔽8)×C22⋊(C127⋊C3), C22×ΓL(1,𝔽8)×C127⋊C3, …
maximal normal subgroup ofA4×ΓL(1,𝔽8)×C127, ΓL(1,𝔽8)×C22⋊(C127⋊C3), C22×ΓL(1,𝔽8)×C127⋊C3, …
maximal quotient ofC22×C7⋊C9×C127, C2×D3×ΓL(1,𝔽8)×C127, C22×C3×ΓL(1,𝔽8)×C127

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10668, 71);