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C3×C5×C3⋊AGL(1,𝔽23) #36384753

order22770
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C3⋊AGL(1,𝔽23)
unambiguous semidirect productC3⋊(C3×C5×AGL(1,𝔽23))
unambiguous semidirect productD69⋊(C3×C5×C11)
unambiguous semidirect product(C23⋊C11)⋊(C3×C5×D3)
unambiguous semidirect product(C3×D69)⋊(C5×C11)
unambiguous semidirect product(C5×D69)⋊(C3×C11)
unambiguous semidirect product(C3×C5×D69)⋊C11

Splittings

Fitting, socle, HallC32×C5×C23 ⋊ C2×C11
derivedC3×C23 ⋊ C2×C3×C5×C11
HallC32×C5×C23⋊C11 ⋊ C2
HallC32×C23⋊C11 ⋊ C2×C5
HallC3×C5×D69 ⋊ C11
HallC5×C23⋊C11 ⋊ C3×D3
HallC3×D69 ⋊ C5×C11
HallC23⋊C11 ⋊ C3×C5×D3
HallC32×C23 ⋊ C2×C5×C11
HallC5×C23 ⋊ C3×D3×C11
HallC32×C5 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C3×C5×D3×C11
SylowC32 ⋊ C5×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC3×C23C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22770, 37);