Finite Group Databasebeta

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C2×C7×#13133724 #37558811

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

Aliases

direct productC2×C7×#13133724

Splittings

Fitting, socle, HallC2×C7×C11×C31 ⋊ C5
derived, HallC11×C31 ⋊ C2×C5×C7
HallC7×C11×C31 ⋊ C2×C5
HallC2×C11×C31 ⋊ C5×C7
HallC2×C7×C31 ⋊ C11⋊C5
HallC7×C31 ⋊ C2×C11⋊C5
HallC2×C7×C11 ⋊ ΓL(1,𝔽32)
HallC7×C11 ⋊ C2×ΓL(1,𝔽32)
HallC2×C31 ⋊ C7×C11⋊C5
SylowC31 ⋊ C2×C7×C11⋊C5
HallC2×C11 ⋊ C7×ΓL(1,𝔽32)
SylowC11 ⋊ C2×C7×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C7#13133724
commutator, cosocle, hypocenterC11×C31C2×C5×C7
FrattiniC1G
Fitting, socleC2×C7×C11×C31C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4774

Conjugacy classes & character table

1022 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 7);