Finite Group Databasebeta

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D7×#13133724 #37558850

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

Aliases

direct productD7×#13133724
unambiguous semidirect productC7⋊(C2×#13133724)

Splittings

Fitting, socle, derived, HallC7×C11×C31 ⋊ C2×C5
HallC7×#13133724 ⋊ C2
HallC11×D7×C31 ⋊ C5
HallD7×C31 ⋊ C11⋊C5
HallC11×C31 ⋊ C5×D7
HallC7×C31 ⋊ C2×C11⋊C5
HallC11×D7 ⋊ ΓL(1,𝔽32)
HallC7×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ D7×C11⋊C5
SylowC11 ⋊ D7×ΓL(1,𝔽32)
SylowC7 ⋊ C2×#13133724

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C31C2×C5
LCSG ▷ C7×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 46);