Finite Group Databasebeta

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C7×C31×AGL(1,𝔽11) #37558834

order23870
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC7×C31×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C7×C31)
unambiguous semidirect product(C11⋊C5)⋊(C2×C7×C31)
unambiguous semidirect product(C7×D11)⋊(C5×C31)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C7×C31
HallC7×C31×C11⋊C5 ⋊ C2
HallC7×D11×C31 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×C7
HallD11×C31 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C2×C5×C7
HallC7×D11 ⋊ C5×C31
HallC7×C11 ⋊ C2×C5×C31
HallC11⋊C5 ⋊ C2×C7×C31
HallD11 ⋊ C5×C7×C31

Subgroups

subgroupG/H
center, hypercenterC7×C31AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C5×C7×C31
FrattiniC1G
Fitting, socleC7×C11×C31C2×C5
LCSG ▷ C11
UCSC1 ◁ C7×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

2387 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 30);