Finite Group Databasebeta

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C7×(C11⋊C5)⋊D31 #37558840

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

Aliases

direct productC7×(C11⋊C5)⋊D31
unambiguous semidirect product(C11⋊C5)⋊(C7×D31)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C5×C7
HallC7×C31×C11⋊C5 ⋊ C2
HallC7×D341 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×C7
HallD341 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ D31
HallC7×C31 ⋊ AGL(1,𝔽11)
HallC7×C11 ⋊ C5×D31
HallC11⋊C5 ⋊ C7×D31
SylowC31 ⋊ C7×AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D31

Subgroups

subgroupG/H
center, hypercenterC7(C11⋊C5)⋊D31
commutator, cosocle, hypocenterC11×C31C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 36);