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C5×ΓL(1,𝔽8)×D113 #37557550

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D113
unambiguous semidirect productC113⋊(C2×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D113)⋊(C3×C5)
unambiguous semidirect product(C5×C7×D113)⋊C3

Splittings

Fitting, socle, HallC5×C7×C113 ⋊ C2×C3
derived, HallC7×C113 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C113 ⋊ C2
HallC5×C7×D113 ⋊ C3
HallΓL(1,𝔽8)×C113 ⋊ C2×C5
HallC7×D113 ⋊ C3×C5
HallC5×C113 ⋊ C2×ΓL(1,𝔽8)
SylowC113 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D113
SylowC7 ⋊ C3×C5×D113

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D113
commutator, cosocle, hypocenterC7×C113C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C113C2×C3
LCSG ▷ C7×C113
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3955

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 26);