Finite Group Databasebeta

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C2×#14558652⋊C5 #37558164

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×#14558652⋊C5
unambiguous semidirect product(C2×#14558652)⋊C5

Splittings

Fitting, socle, HallC2×C13×C61 ⋊ C3×C5
derived, HallC13×C61 ⋊ C2×C3×C5
HallC2×C13×C61⋊C5 ⋊ C3
HallC2×#14558652 ⋊ C5
HallC13×C61⋊C5 ⋊ C2×C3
Hall#14558652 ⋊ C2×C5
HallC2×C61⋊C5 ⋊ C13⋊C3
HallC61⋊C5 ⋊ C2×C13⋊C3
HallC2×C61 ⋊ C5×C13⋊C3
SylowC61 ⋊ C2×C5×C13⋊C3
HallC2×C13 ⋊ (C61⋊C3)⋊C5
SylowC13 ⋊ C2×(C61⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#14558652⋊C5
commutator, cosocle, hypocenterC13×C61C2×C3×C5
FrattiniC1G
Fitting, socleC2×C13×C61C3×C5
LCSG ▷ C13×C61
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1586

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 9);