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C4×ΓL(1,𝔽8)×C103 #22575730

order8652
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C4×C103 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C103
unambiguous semidirect product(C4×C7)⋊(C3×C103)

Splittings

Fitting, HallC4×C7×C103 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C103
HallC7×C103 ⋊ C3×C4
HallC4×C7 ⋊ C3×C103

Subgroups

subgroupG/H
center, hypercenterC4×C103ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C103
FrattiniC2C2×ΓL(1,𝔽8)×C103
FittingC4×C7×C103C3
socleC2×C7×C103C2×C3
LCSG ▷ C7
UCSC1 ◁ C4×C103

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2060 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×ΓL(1,𝔽8)×C103⋊C3, Dic3×ΓL(1,𝔽8)×C103, C3×C4×ΓL(1,𝔽8)×C103
maximal normal subgroup ofC4×ΓL(1,𝔽8)×C103⋊C3, C3×C4×ΓL(1,𝔽8)×C103
maximal quotient ofC4×C7⋊C9×C103, Dic3×ΓL(1,𝔽8)×C103, C3×C4×ΓL(1,𝔽8)×C103

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 3);