Finite Group Databasebeta

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C3×C4×C11×C23⋊C11 #45688979

order33396
automorphism?
homologyAbelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC3×C4×C11×C23⋊C11
unambiguous semidirect product(C4×C23)⋊(C3×C112)
unambiguous semidirect product(C3×C4×C23)⋊C112
unambiguous semidirect product(C4×C11×C23)⋊(C3×C11)
unambiguous semidirect product(C3×C4×C11×C23)⋊C11

Splittings

FittingC3×C4×C11×C23 ⋊ C11
derived, SylowC23 ⋊ C3×C4×C112
HallC3×C4×C23 ⋊ C112
HallC4×C23 ⋊ C3×C112
HallC3×C23 ⋊ C4×C112

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11C23⋊C11
commutator, hypocenterC23C3×C4×C112
FrattiniC2C2×C3×C11×C23⋊C11
FittingC3×C4×C11×C23C11
socleC2×C3×C11×C23C2×C11
prime radicalC2×C3×C11×C23⋊C11C2
cosocleC2×C23C2×C3×C112
LCSG ▷ C23
UCSC1 ◁ C3×C4×C11

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 43);