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C5×ΓL(1,𝔽8)×A5 #20263174

order6300
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×ΓL(1,𝔽8)×A5
unambiguous semidirect productC7⋊(C3×C5×A5)
unambiguous semidirect product(C5×C7)⋊(C3×A5)
unambiguous semidirect product(C7×A5)⋊(C3×C5)
unambiguous semidirect product(C5×C7×A5)⋊C3

Splittings

FittingC5×C7 ⋊ C3×A5
socleC5×C7×A5 ⋊ C3
derivedC7×A5 ⋊ C3×C5
SylowC7 ⋊ C3×C5×A5

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×A5
commutator, hypocenterC7×A5C3×C5
FrattiniC1G
FittingC5×C7C3×A5
socleC5×C7×A5C3
LCSG ▷ C7×A5
UCSC1 ◁ C5

92 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6300, 570);