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C2×D23⋊C121 #26013299

order11132
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D23⋊C121
unambiguous semidirect productD23⋊(C2×C121)
unambiguous semidirect product(C2×D23)⋊C121
unambiguous semidirect product(C23⋊C121)⋊C22
unambiguous semidirect product(C2×C23⋊C121)⋊C2

Splittings

derived, SylowC23 ⋊ C22×C121
HallC23⋊C121 ⋊ C22
HallC2×D23 ⋊ C121

Subgroups

subgroupG/H
center, hypercenterC2×C11AGL(1,𝔽23)
commutator, hypocenterC23C22×C121
FrattiniC11C2×AGL(1,𝔽23)
Fitting, socleC2×C11×C23C2×C11
prime radicalC2×C11×D23C11
cosocleC11×C23C22×C11
LCSG ▷ C23
UCSC1 ◁ C2×C11

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D23⋊C121, C2×C3×D23⋊C121, C2×C3⋊(D23⋊C121)
maximal normal subgroup ofC2×C3×D23⋊C121
maximal quotient ofD3×D23⋊C121, C2×C3×D23⋊C121, C2×C3⋊(D23⋊C121)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11132, 8);