Finite Group Databasebeta

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C3×C11⋊C5×C149 #37589634

order24585
automorphism?
homologyAbelianization (H1) = C3×C5×C149 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×C149
unambiguous semidirect productC11⋊(C3×C5×C149)
unambiguous semidirect product(C3×C11)⋊(C5×C149)
unambiguous semidirect product(C11×C149)⋊(C3×C5)
unambiguous semidirect product(C3×C11×C149)⋊C5

Splittings

Fitting, socle, HallC3×C11×C149 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C149
HallC11×C149 ⋊ C3×C5
HallC3×C11 ⋊ C5×C149

Subgroups

subgroupG/H
center, hypercenterC3×C149C11⋊C5
commutator, cosocle, hypocenterC11C3×C5×C149
FrattiniC1G
Fitting, socleC3×C11×C149C5
LCSG ▷ C11
UCSC1 ◁ C3×C149

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4917

Conjugacy classes & character table

3129 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24585, 2);