Finite Group Databasebeta

← Prev (#44567389) Next (#44567391) →

C3×C5×A4×C179 #44567390

order32220
automorphism?
homologyAbelianization (H1) = C32×C5×C179 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×A4×C179
unambiguous semidirect productC22⋊(C32×C5×C179)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C179)
unambiguous semidirect product(C22×C5)⋊(C32×C179)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C179)
unambiguous semidirect product(C22×C179)⋊(C32×C5)
unambiguous semidirect product(C22×C3×C179)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C179)⋊C32
unambiguous semidirect product(C22×C3×C5×C179)⋊C3

Splittings

Fitting, socleC22×C3×C5×C179 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C179
HallC22×C5×C179 ⋊ C32
HallC22×C179 ⋊ C32×C5
HallC22×C5 ⋊ C32×C179

Subgroups

subgroupG/H
center, hypercenterC3×C5×C179A4
commutator, cosocle, hypocenterC22C32×C5×C179
FrattiniC1G
Fitting, socleC22×C3×C5×C179C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C179

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10740

Conjugacy classes & character table

10740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 77);