Finite Group Databasebeta

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C3×C3⋊(C5⋊AGL(1,𝔽23)) #36384755

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

Aliases

direct productC3×C3⋊(C5⋊AGL(1,𝔽23))
unambiguous semidirect productC3⋊(C3×C5⋊AGL(1,𝔽23))
unambiguous semidirect productC5⋊(C3×C3⋊AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊(C3×D15)
unambiguous semidirect productD345⋊(C3×C11)
unambiguous semidirect product(C3×D345)⋊C11

Splittings

Fitting, socle, HallC32×C5×C23 ⋊ C2×C11
derivedC3×C5×C23 ⋊ C2×C3×C11
HallC32×C5×C23⋊C11 ⋊ C2
HallC32×C23⋊C11 ⋊ D5
HallC3×D345 ⋊ C11
HallC5×C23⋊C11 ⋊ C3×D3
HallC23⋊C11 ⋊ C3×D15
HallC32×C23 ⋊ D5×C11
HallC5×C23 ⋊ C3×D3×C11
HallC32×C5 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C3×C11×D15
SylowC32 ⋊ C5⋊AGL(1,𝔽23)
SylowC5 ⋊ C3×C3⋊AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C5⋊AGL(1,𝔽23))
commutator, cosocle, hypocenterC3×C5×C23C2×C3×C11
FrattiniC1G
Fitting, socleC32×C5×C23C2×C11
LCSG ▷ C3×C5×C23
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22770, 39);