Finite Group Databasebeta

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C7×D11×ΓL(1,𝔽32) #37558833

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

Aliases

direct productC7×D11×ΓL(1,𝔽32)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C5×C7
HallC7×C11×ΓL(1,𝔽32) ⋊ C2
HallC7×D11×C31 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C7
HallD11×C31 ⋊ C5×C7
HallC7×C31 ⋊ C5×D11
HallC7×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C7×D11
SylowC11 ⋊ C2×C7×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC7D11×ΓL(1,𝔽32)
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 29);