Finite Group Databasebeta

← Prev (#38784650) Next (#38784652) →

ΓL(1,𝔽8)×C3⋊(D29⋊C7) #38784651

order25578
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C3⋊(D29⋊C7)
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)×D29⋊C7)
unambiguous semidirect productD87⋊(C7×ΓL(1,𝔽8))
unambiguous semidirect product(C29⋊C7)⋊(D3×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D87)⋊C7
unambiguous semidirect product(C7×C3⋊(D29⋊C7))⋊C3

Splittings

Fitting, socle, derivedC3×C7×C29 ⋊ C2×C3×C7
HallC3×ΓL(1,𝔽8)×C29⋊C7 ⋊ C2
HallC7×C29⋊C7 ⋊ C3×D3
SylowC29 ⋊ D3×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C29C2×C3×C7
LCSG ▷ C3×C7×C29
UCSC1

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 609

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25578, 95);