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C3×ΓL(1,𝔽32)⋊D11 #23779443

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

Aliases

direct productC3×ΓL(1,𝔽32)⋊D11

Splittings

Fitting, socle, HallC3×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C3×C5
HallC3×C11×ΓL(1,𝔽32) ⋊ C2
HallC3×D341 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C3
HallD341 ⋊ C3×C5
HallC3×ΓL(1,𝔽32) ⋊ D11
HallΓL(1,𝔽32) ⋊ C3×D11
HallC3×C31 ⋊ C5×D11
HallC3×C11 ⋊ D31⋊C5
SylowC31 ⋊ C3×C5×D11
SylowC11 ⋊ C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽32)⋊D11
commutator, cosocle, hypocenterC11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D11×D31⋊C5, D3×ΓL(1,𝔽32)⋊D11, (C3⋊(D31⋊C5))⋊D11, …
maximal normal subgroup ofC3×D11×D31⋊C5, D3×ΓL(1,𝔽32)⋊D11, (C3⋊(D31⋊C5))⋊D11, …
maximal quotient ofC3×ΓL(1,𝔽32)⋊Dic11, C2×C3×ΓL(1,𝔽32)⋊D11, C9×ΓL(1,𝔽32)⋊D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 42);