Finite Group Databasebeta

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C11⋊C5×D213 #37552899

order23430
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D213
unambiguous semidirect productC3⋊(C11⋊C5×D71)

Splittings

Fitting, socle, derived, HallC3×C11×C71 ⋊ C2×C5
HallC3×C11⋊C5×C71 ⋊ C2
HallC11×D213 ⋊ C5
HallC11⋊C5×C71 ⋊ D3
HallC11×C71 ⋊ C5×D3
HallC3×C71 ⋊ C2×C11⋊C5
HallC3×C11⋊C5 ⋊ D71
SylowC71 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D71
SylowC11 ⋊ C5×D213
SylowC3 ⋊ C11⋊C5×D71

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C71C2×C5
LCSG ▷ C3×C11×C71
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 48);