Finite Group Databasebeta

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C3×C5×A4×C149 #41001315

order26820
automorphism?
homologyAbelianization (H1) = C32×C5×C149 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×A4×C149
unambiguous semidirect productC22⋊(C32×C5×C149)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C149)
unambiguous semidirect product(C22×C5)⋊(C32×C149)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C149)
unambiguous semidirect product(C22×C149)⋊(C32×C5)
unambiguous semidirect product(C22×C3×C149)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C149)⋊C32
unambiguous semidirect product(C22×C3×C5×C149)⋊C3

Splittings

Fitting, socleC22×C3×C5×C149 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C149
HallC22×C5×C149 ⋊ C32
HallC22×C149 ⋊ C32×C5
HallC22×C5 ⋊ C32×C149

Subgroups

subgroupG/H
center, hypercenterC3×C5×C149A4
commutator, cosocle, hypocenterC22C32×C5×C149
FrattiniC1G
Fitting, socleC22×C3×C5×C149C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C149

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8940

Conjugacy classes & character table

8940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 101);