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C5×C3⋊(C3⋊AGL(1,𝔽23)) #36384757

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

Aliases

direct productC5×C3⋊(C3⋊AGL(1,𝔽23))
unambiguous semidirect productC3⋊(C5×C3⋊AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊(C5×C3⋊D3)
unambiguous semidirect product(C3⋊D69)⋊(C5×C11)
unambiguous semidirect product(C5×C3⋊D69)⋊C11

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊AGL(1,𝔽23))
commutator, cosocle, hypocenterC32×C23C2×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C23C2×C11
LCSG ▷ C32×C23
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1035

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22770, 41);