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D5×ΓL(1,𝔽8)×C113 #37557553

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C113 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C113
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C113)
unambiguous semidirect product(C7×D5)⋊(C3×C113)
unambiguous semidirect product(C7×D5×C113)⋊C3

Splittings

Fitting, socle, HallC5×C7×C113 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C113
HallC5×ΓL(1,𝔽8)×C113 ⋊ C2
HallC7×D5×C113 ⋊ C3
HallC7×C113 ⋊ C3×D5
HallC5×C113 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C113
HallC7×D5 ⋊ C3×C113
SylowC7 ⋊ C3×D5×C113
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C113

Subgroups

subgroupG/H
center, hypercenterC113D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C113
FrattiniC1G
Fitting, socleC5×C7×C113C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C113

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3955

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 29);