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C32×C5⋊AGL(1,𝔽23) #36384751

order22770
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5⋊AGL(1,𝔽23)
unambiguous semidirect productC5⋊(C32×AGL(1,𝔽23))
unambiguous semidirect productD115⋊(C32×C11)
unambiguous semidirect product(C23⋊C11)⋊(C32×D5)
unambiguous semidirect product(C3×D115)⋊(C3×C11)
unambiguous semidirect product(C32×D115)⋊C11

Splittings

Fitting, socle, HallC32×C5×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C2×C32×C11
HallC32×C5×C23⋊C11 ⋊ C2
HallC32×C23⋊C11 ⋊ D5
HallC32×D115 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×C32
HallC23⋊C11 ⋊ C32×D5
HallD115 ⋊ C32×C11
HallC32×C23 ⋊ D5×C11
HallC32×C5 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C32×D5×C11
SylowC5 ⋊ C32×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC32C5⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC5×C23C2×C32×C11
FrattiniC1G
Fitting, socleC32×C5×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1035

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22770, 35);