Finite Group Databasebeta

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C2×D3×C11×C23⋊C11 #45689010

order33396
automorphism?
homologyAbelianization (H1) = C22×C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×D3×C11×C23⋊C11
unambiguous semidirect productC3⋊(C22×C11×C23⋊C11)
unambiguous semidirect product(C2×C3)⋊(C2×C11×C23⋊C11)
unambiguous semidirect product(C2×D3×C23)⋊C112
unambiguous semidirect product(C2×D3×C11×C23)⋊C11

Splittings

Fitting, socleC2×C3×C11×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C22×C112
HallC3×C11×C23⋊C11 ⋊ C22
HallC2×D3×C23 ⋊ C112
SylowC23 ⋊ C2×D3×C112
SylowC3 ⋊ C22×C11×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×C23⋊C11
commutator, cosocle, hypocenterC3×C23C22×C112
FrattiniC1G
Fitting, socleC2×C3×C11×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C2×C11

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1518

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 74);