Finite Group Databasebeta

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D7×#14555918 #44538948

order31570
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD7×#14555918
unambiguous semidirect productC7⋊(C2×#14555918)

Splittings

Fitting, socle, derived, HallC7×C11×C41 ⋊ C2×C5
HallC7×#14555918 ⋊ C2
HallC11×D7×C41 ⋊ C5
HallD7×C41 ⋊ C11⋊C5
HallC11×C41 ⋊ C5×D7
HallC7×C41 ⋊ C2×C11⋊C5
HallC11×D7 ⋊ C41⋊C5
HallC7×C11 ⋊ C2×C41⋊C5
SylowC41 ⋊ D7×C11⋊C5
SylowC11 ⋊ D7×C41⋊C5
SylowC7 ⋊ C2×#14555918

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C41C2×C5
LCSG ▷ C7×C11×C41
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31570, 45);