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C2×C3⋊(C11⋊AGL(1,𝔽23)) #45689011

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

Aliases

direct productC2×C3⋊(C11⋊AGL(1,𝔽23))
unambiguous semidirect product(C2×C3)⋊(C11⋊AGL(1,𝔽23))
unambiguous semidirect product(C2×C11)⋊(C3⋊AGL(1,𝔽23))
unambiguous semidirect product(C2×C23⋊C11)⋊D33
unambiguous semidirect product(C2×D759)⋊C11

Splittings

Fitting, socleC2×C3×C11×C23 ⋊ C2×C11
derivedC3×C11×C23 ⋊ C22×C11
HallC3×C11×C23⋊C11 ⋊ C22
HallC11×C23⋊C11 ⋊ C2×D3
HallC3×C23 ⋊ C2×C11×D11
SylowC23 ⋊ C2×C11×D33
SylowC3 ⋊ C2×C11⋊AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C11⋊AGL(1,𝔽23))
commutator, cosocle, hypocenterC3×C11×C23C22×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C23C2×C11
LCSG ▷ C3×C11×C23
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1518

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 75);