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C52×C3⋊AGL(1,𝔽23) #49182108

order37950
automorphism?
homologyAbelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊AGL(1,𝔽23)
unambiguous semidirect productC3⋊(C52×AGL(1,𝔽23))
unambiguous semidirect productD69⋊(C52×C11)
unambiguous semidirect product(C23⋊C11)⋊(C52×D3)
unambiguous semidirect product(C5×D69)⋊(C5×C11)
unambiguous semidirect product(C52×D69)⋊C11

Splittings

Fitting, socle, HallC3×C52×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C2×C52×C11
HallC3×C52×C23⋊C11 ⋊ C2
HallC52×C23⋊C11 ⋊ D3
HallC52×D69 ⋊ C11
HallC3×C23⋊C11 ⋊ C2×C52
HallC52×C23 ⋊ D3×C11
HallC23⋊C11 ⋊ C52×D3
HallD69 ⋊ C52×C11
HallC3×C52 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C52×D3×C11
SylowC3 ⋊ C52×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC52C3⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC3×C23C2×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1725

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 45);