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C2×C5×C3⋊AGL(1,𝔽23) #29503263

order15180
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C3⋊AGL(1,𝔽23)
unambiguous semidirect product(C2×C3)⋊(C5×AGL(1,𝔽23))
unambiguous semidirect product(C2×D69)⋊(C5×C11)
unambiguous semidirect product(C2×C23⋊C11)⋊(C5×D3)
unambiguous semidirect product(C2×C5×D69)⋊C11

Splittings

Fitting, socleC2×C3×C5×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C22×C5×C11
HallC3×C5×C23⋊C11 ⋊ C22
HallC2×C5×D69 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×D3
HallC3×C23⋊C11 ⋊ C22×C5
HallC3×C5×C23 ⋊ C22×C11
HallC2×D69 ⋊ C5×C11
HallC23⋊C11 ⋊ C2×C5×D3
HallC5×C23 ⋊ C2×D3×C11
SylowC23 ⋊ C2×C5×D3×C11
HallC3×C5 ⋊ C2×AGL(1,𝔽23)
SylowC3 ⋊ C2×C5×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC3×C23C22×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 49);