Finite Group Databasebeta

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C2×C5×C9×D179 #44567341

order32220
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D179
unambiguous semidirect productC179⋊(C22×C5×C9)
unambiguous semidirect product(C2×C179)⋊(C2×C5×C9)

Splittings

FittingC2×C5×C9×C179 ⋊ C2
derived, SylowC179 ⋊ C22×C5×C9
HallC5×C9×C179 ⋊ C22
HallC9×C179 ⋊ C22×C5
HallC5×C179 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D179
commutator, hypocenterC179C22×C5×C9
FrattiniC3C2×C3×C5×D179
FittingC2×C5×C9×C179C2
socleC2×C3×C5×C179C2×C3
prime radicalC2×C3×C5×D179C3
cosocleC3×C179C22×C3×C5
LCSG ▷ C179
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16110

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 28);