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C5×Dic9×C179 #44567318

order32220
automorphism?
homologyAbelianization (H1) = C4×C5×C179 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic9×C179
unambiguous semidirect productC9⋊(C4×C5×C179)

Splittings

derived, SylowC9 ⋊ C4×C5×C179
HallC5×C9×C179 ⋊ C4
HallC9×C179 ⋊ C4×C5
HallC5×C9 ⋊ C4×C179

Subgroups

subgroupG/H
center, hypercenterC2×C5×C179D9
commutator, hypocenterC9C4×C5×C179
FrattiniC2×C3C5×D3×C179
FittingC2×C5×C9×C179C2
socle, prime radicalC2×C3×C5×C179D3
cosocleC2×C9C2×C5×C179
LCSG ▷ C9
UCSC1 ◁ C2×C5×C179

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32220

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, 5);