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A4×ΓL(1,𝔽8)×C107 #41004114

order26964
automorphism?
homologyAbelianization (H1) = C32×C107 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×ΓL(1,𝔽8)×C107
unambiguous semidirect product(C22×ΓL(1,𝔽8))⋊(C3×C107)
unambiguous semidirect product(C7×A4)⋊(C3×C107)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8))⋊(C3×C107)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8)×C107)⋊C3
unambiguous semidirect product(C7×A4×C107)⋊C3
unambiguous semidirect product(C22×ΓL(1,𝔽8)×C107)⋊C3

Splittings

Fitting, socle, HallC22×C7×C107 ⋊ C32
derived, HallC22×C7 ⋊ C32×C107
HallC7×C107 ⋊ C3×A4
HallC22×C107 ⋊ C3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×A4×C107
SylowC22 ⋊ C3×ΓL(1,𝔽8)×C107

Subgroups

subgroupG/H
center, hypercenterC107A4×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C107
FrattiniC1G
Fitting, socleC22×C7×C107C32
LCSG ▷ C22×C7
UCSC1 ◁ C107

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2996

Conjugacy classes & character table

2140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 63);