Finite Group Databasebeta

← Prev (#44567339) Next (#44567341) →

C2×C9×D5×C179 #44567340

order32220
automorphism?
homologyAbelianization (H1) = C22×C9×C179 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D5×C179
unambiguous semidirect productC5⋊(C22×C9×C179)
unambiguous semidirect product(C2×C5)⋊(C2×C9×C179)

Splittings

FittingC2×C5×C9×C179 ⋊ C2
derived, SylowC5 ⋊ C22×C9×C179
HallC5×C9×C179 ⋊ C22
HallC5×C179 ⋊ C22×C9
HallC5×C9 ⋊ C22×C179

Subgroups

subgroupG/H
center, hypercenterC2×C9×C179D5
commutator, hypocenterC5C22×C9×C179
FrattiniC3C2×C3×D5×C179
FittingC2×C5×C9×C179C2
socleC2×C3×C5×C179C2×C3
prime radicalC2×C3×D5×C179C3
cosocleC3×C5C22×C3×C179
LCSG ▷ C5
UCSC1 ◁ C2×C9×C179

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16110

Conjugacy classes & character table

12888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 27);