Finite Group Databasebeta

← Prev (#37557526) Next (#37557528) →

C2×C5×ΓL(1,𝔽8)×C113 #37557527

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C113 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C113
unambiguous semidirect product(C2×C7)⋊(C3×C5×C113)
unambiguous semidirect product(C2×C5×C7)⋊(C3×C113)
unambiguous semidirect product(C2×C7×C113)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×C113)⋊C3

Splittings

Fitting, socle, HallC2×C5×C7×C113 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C5×C113
HallC5×C7×C113 ⋊ C2×C3
HallC2×C7×C113 ⋊ C3×C5
HallC7×C113 ⋊ C2×C3×C5
HallC2×C5×C7 ⋊ C3×C113
HallC5×C7 ⋊ C2×C3×C113
HallC2×C7 ⋊ C3×C5×C113

Subgroups

subgroupG/H
center, hypercenterC2×C5×C113ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C5×C113
FrattiniC1G
Fitting, socleC2×C5×C7×C113C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C113

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7910

Conjugacy classes & character table

5650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 3);