Finite Group Databasebeta

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C2×C3×#16840849 #37552856

order23430
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×#16840849

Splittings

Fitting, socle, HallC2×C3×C11×C71 ⋊ C5
derived, HallC11×C71 ⋊ C2×C3×C5
HallC3×C11×C71 ⋊ C2×C5
HallC2×C11×C71 ⋊ C3×C5
HallC2×C3×C71 ⋊ C11⋊C5
HallC3×C71 ⋊ C2×C11⋊C5
HallC2×C71 ⋊ C3×C11⋊C5
SylowC71 ⋊ C2×C3×C11⋊C5
HallC2×C3×C11 ⋊ C71⋊C5
HallC3×C11 ⋊ C2×C71⋊C5
HallC2×C11 ⋊ C3×C71⋊C5
SylowC11 ⋊ C2×C3×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3#16840849
commutator, cosocle, hypocenterC11×C71C2×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C71C5
LCSG ▷ C11×C71
UCSC1 ◁ C2×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4686

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 5);