Finite Group Databasebeta

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C3×C11×C23⋊C11 #22552504

order8349
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C3×C112 · Schur multiplier (H2) = C11

Aliases

direct productC3×C11×C23⋊C11
unambiguous semidirect productC23⋊(C3×C112)
unambiguous semidirect product(C3×C23)⋊C112
unambiguous semidirect product(C11×C23)⋊(C3×C11)
unambiguous semidirect product(C3×C11×C23)⋊C11

Splittings

Fitting, socleC3×C11×C23 ⋊ C11
derived, SylowC23 ⋊ C3×C112
HallC3×C23 ⋊ C112

Subgroups

subgroupG/H
center, hypercenterC3×C11C23⋊C11
commutator, hypocenterC23C3×C112
FrattiniC1G
Fitting, socleC3×C11×C23C11
LCSG ▷ C23
UCSC1 ◁ C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

429 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×AGL(1,𝔽23), C3×C11⋊AGL(1,𝔽23), C3×D11×C23⋊C11, …
maximal normal subgroup ofC3×C11×AGL(1,𝔽23), C3×C11⋊AGL(1,𝔽23), C3×D11×C23⋊C11, …
maximal quotient ofC2×C3×C11×C23⋊C11, C9×C11×C23⋊C11, C32×C11×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8349, 4);