Finite Group Databasebeta

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C3×C52×AGL(1,𝔽23) #49182103

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C3×C52×C11)
unambiguous semidirect product(C3×D23)⋊(C52×C11)
unambiguous semidirect product(C5×D23)⋊(C3×C5×C11)
unambiguous semidirect product(C23⋊C11)⋊(C2×C3×C52)
unambiguous semidirect product(C3×C5×D23)⋊(C5×C11)
unambiguous semidirect product(C3×C52×D23)⋊C11

Splittings

Fitting, socle, HallC3×C52×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C3×C52×C11
HallC3×C52×C23⋊C11 ⋊ C2
HallC52×C23⋊C11 ⋊ C2×C3
HallC3×C52×D23 ⋊ C11
HallC52×D23 ⋊ C3×C11
HallC3×C23⋊C11 ⋊ C2×C52
HallC52×C23 ⋊ C2×C3×C11
HallC23⋊C11 ⋊ C2×C3×C52
HallC3×D23 ⋊ C52×C11
HallC3×C23 ⋊ C2×C52×C11
HallD23 ⋊ C3×C52×C11

Subgroups

subgroupG/H
center, hypercenterC3×C52AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C2×C3×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C3×C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1725

Conjugacy classes & character table

1725 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 40);