Finite Group Databasebeta

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C31×C7⋊AGL(1,𝔽11) #37558858

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

Aliases

direct productC31×C7⋊AGL(1,𝔽11)
unambiguous semidirect productC7⋊(C31×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D7×C31)
unambiguous semidirect productD77⋊(C5×C31)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C31
HallC7×C31×C11⋊C5 ⋊ C2
HallC31×D77 ⋊ C5
HallC31×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C5×D7
HallC7×C31 ⋊ AGL(1,𝔽11)
HallD77 ⋊ C5×C31
HallC11⋊C5 ⋊ D7×C31
SylowC11 ⋊ C5×D7×C31
SylowC7 ⋊ C31×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC31C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C5×C31
FrattiniC1G
Fitting, socleC7×C11×C31C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 54);