Finite Group Databasebeta

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C3×ΓL(1,𝔽8)×D205 #38788959

order25830
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D205
unambiguous semidirect productC5⋊(C3×ΓL(1,𝔽8)×D41)
unambiguous semidirect productC41⋊(C3×D5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D205)⋊C32
unambiguous semidirect product(C3×C7×D205)⋊C3

Splittings

Fitting, socleC3×C5×C7×C41 ⋊ C2×C3
derived, HallC5×C7×C41 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8)×C41 ⋊ C2
HallC7×D205 ⋊ C32
HallC3×ΓL(1,𝔽8)×C41 ⋊ D5
HallC3×C5×ΓL(1,𝔽8) ⋊ D41
HallC7×C41 ⋊ C32×D5
HallC5×C41 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC41 ⋊ C3×D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×D41
SylowC7 ⋊ C32×D205
SylowC5 ⋊ C3×ΓL(1,𝔽8)×D41

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D205
commutator, cosocle, hypocenterC5×C7×C41C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2×C3
LCSG ▷ C5×C7×C41
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4305

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 63);