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C2×ΓL(1,𝔽8)×C373 #30627822

order15666
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C3×C373 · Schur multiplier (H2) = C1

Aliases

direct productC2×ΓL(1,𝔽8)×C373
unambiguous semidirect product(C2×C7)⋊(C3×C373)

Splittings

Fitting, socle, HallC2×C7×C373 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C373
HallC7×C373 ⋊ C2×C3
HallC2×C7 ⋊ C3×C373

Subgroups

subgroupG/H
center, hypercenterC2×C373ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C373
FrattiniC1G
Fitting, socleC2×C7×C373C3
LCSG ▷ C7
UCSC1 ◁ C2×C373

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5222

Conjugacy classes & character table

3730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×ΓL(1,𝔽8)×C373, ΓL(1,𝔽8)×Dic373, ΓL(1,𝔽8)⋊C4×C373, …
maximal normal subgroup ofC4×ΓL(1,𝔽8)×C373, ΓL(1,𝔽8)×Dic373, ΓL(1,𝔽8)⋊C4×C373, …
maximal quotient ofC4×ΓL(1,𝔽8)×C373, C22×ΓL(1,𝔽8)×C373

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15666, 3);