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C3×ΓL(1,𝔽8)×D29⋊C7 #38784648

order25578
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D29⋊C7
unambiguous semidirect productD29⋊(C3×C7×ΓL(1,𝔽8))
unambiguous semidirect product(C3×D29)⋊(C7×ΓL(1,𝔽8))
unambiguous semidirect product(C29⋊C7)⋊(C2×C3×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D29)⋊(C3×C7)
unambiguous semidirect product(C7×D29⋊C7)⋊C32
unambiguous semidirect product(C3×ΓL(1,𝔽8)×D29)⋊C7
unambiguous semidirect product(C3×C7×D29⋊C7)⋊C3

Splittings

Fitting, socleC3×C7×C29 ⋊ C2×C3×C7
derivedC7×C29 ⋊ C2×C32×C7
HallC3×ΓL(1,𝔽8)×C29⋊C7 ⋊ C2
HallC7×D29⋊C7 ⋊ C32
HallC7×C29⋊C7 ⋊ C2×C32
HallD29 ⋊ C3×C7×ΓL(1,𝔽8)
SylowC29 ⋊ C2×C3×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D29⋊C7
commutator, cosocle, hypocenterC7×C29C2×C32×C7
FrattiniC1G
Fitting, socleC3×C7×C29C2×C3×C7
LCSG ▷ C7×C29
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 609

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25578, 92);