Finite Group Databasebeta

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C7×C11×D31⋊C5 #37558827

order23870
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D31⋊C5
unambiguous semidirect productD31⋊(C5×C7×C11)
unambiguous semidirect productΓL(1,𝔽32)⋊(C2×C7×C11)
unambiguous semidirect product(C7×D31)⋊(C5×C11)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C2×C5×C7×C11
HallC7×C11×ΓL(1,𝔽32) ⋊ C2
HallC7×C11×D31 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C7
HallC7×ΓL(1,𝔽32) ⋊ C2×C11
HallC11×D31 ⋊ C5×C7
HallC7×D31 ⋊ C5×C11
HallC11×C31 ⋊ C2×C5×C7
HallC7×C31 ⋊ C2×C5×C11
HallΓL(1,𝔽32) ⋊ C2×C7×C11
HallD31 ⋊ C5×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11D31⋊C5
commutator, cosocle, hypocenterC31C2×C5×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

1001 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 23);