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C2×C3×#13133723 #23779406

order10230
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×#13133723

Splittings

Fitting, socle, HallC2×C3×C11×C31 ⋊ C5
derived, HallC11×C31 ⋊ C2×C3×C5
HallC3×C11×C31 ⋊ C2×C5
HallC2×C11×C31 ⋊ C3×C5
HallC2×C3×C31 ⋊ C11⋊C5
HallC3×C31 ⋊ C2×C11⋊C5
HallC2×C3×C11 ⋊ ΓL(1,𝔽32)
HallC2×C31 ⋊ C3×C11⋊C5
HallC3×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ C3×ΓL(1,𝔽32)
SylowC11 ⋊ C2×C3×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C3#13133723
commutator, cosocle, hypocenterC11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C31C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

438 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×#13133723, C3×#20291871, C3×#20291877, …
maximal normal subgroup ofC3×C4×#13133723, C3×#20291871, C3×#20291877, …
maximal quotient ofC3×C4×#13133723, C22×C3×#13133723, C2×C9×#13133723, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 5);