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C2×C3×ΓL(1,𝔽8)×C41⋊C5 #38788941

order25830
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×ΓL(1,𝔽8)×C41⋊C5
unambiguous semidirect product(C2×C7)⋊(C32×C41⋊C5)
unambiguous semidirect product(C2×C3×C7)⋊(C3×C41⋊C5)
unambiguous semidirect product(C2×C41)⋊(C3×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C3×C41)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×ΓL(1,𝔽8)×C41)⋊(C3×C5)
unambiguous semidirect product(C2×C7×C41⋊C5)⋊C32
unambiguous semidirect product(C2×C3×ΓL(1,𝔽8)×C41)⋊C5
unambiguous semidirect product(C2×C3×C7×C41⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C7×C41 ⋊ C3×C5
derived, HallC7×C41 ⋊ C2×C32×C5
HallC2×C3×ΓL(1,𝔽8)×C41 ⋊ C5
HallC2×C7×C41⋊C5 ⋊ C32
HallC3×ΓL(1,𝔽8)×C41 ⋊ C2×C5
HallC7×C41⋊C5 ⋊ C2×C32
HallC2×C7×C41 ⋊ C32×C5
HallC2×C41 ⋊ C3×C5×ΓL(1,𝔽8)
SylowC41 ⋊ C2×C3×C5×ΓL(1,𝔽8)
HallC2×C7 ⋊ C32×C41⋊C5
SylowC7 ⋊ C2×C32×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×C41⋊C5
commutator, cosocle, hypocenterC7×C41C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C7×C41C3×C5
LCSG ▷ C7×C41
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1722

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 45);