Finite Group Databasebeta

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C3×C7×D5×C113 #37557531

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C113 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D5×C113
unambiguous semidirect productC5⋊(C2×C3×C7×C113)

Splittings

Fitting, socle, HallC3×C5×C7×C113 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C7×C113
HallC5×C7×C113 ⋊ C2×C3
HallC3×C5×C113 ⋊ C2×C7
HallC5×C113 ⋊ C2×C3×C7
HallC3×C5×C7 ⋊ C2×C113
HallC5×C7 ⋊ C2×C3×C113
HallC3×C5 ⋊ C2×C7×C113

Subgroups

subgroupG/H
center, hypercenterC3×C7×C113D5
commutator, cosocle, hypocenterC5C2×C3×C7×C113
FrattiniC1G
Fitting, socleC3×C5×C7×C113C2
LCSG ▷ C5
UCSC1 ◁ C3×C7×C113

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11865

Conjugacy classes & character table

9492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 7);