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D11×(C31⋊C3)⋊C5 #23779486

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

Aliases

direct productD11×(C31⋊C3)⋊C5
unambiguous semidirect product(D11×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C2×C3×C5
HallC11×(C31⋊C3)⋊C5 ⋊ C2
HallD11×ΓL(1,𝔽32) ⋊ C3
HallD11×C31⋊C3 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C3
HallC11×C31⋊C3 ⋊ C2×C5
HallD11×C31 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ C3×D11
HallC31⋊C3 ⋊ C5×D11
SylowC31 ⋊ C3×C5×D11
SylowC11 ⋊ C2×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×AGL(1,𝔽31), C2×D11×(C31⋊C3)⋊C5, C3×D11×(C31⋊C3)⋊C5, …
maximal normal subgroup ofD11×AGL(1,𝔽31), C2×D11×(C31⋊C3)⋊C5, C3×D11×(C31⋊C3)⋊C5
maximal quotient ofDic11×(C31⋊C3)⋊C5, C2×D11×(C31⋊C3)⋊C5, D11×ΓL(1,𝔽32)⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 85);