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C179×C9⋊AGL(1,𝔽5) #44567327

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

Aliases

direct productC179×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C179)

Splittings

Fitting, HallC5×C9×C179 ⋊ C4
derived, HallC5×C9 ⋊ C4×C179
HallC9×C179 ⋊ AGL(1,𝔽5)
HallC5×C179 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C179
SylowC5 ⋊ Dic9×C179

Subgroups

subgroupG/H
center, hypercenterC179C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C179
FrattiniC3ΓL(1,𝔽16)×C179
FittingC5×C9×C179C4
socleC3×C5×C179Dic3
prime radicalC3×D5×C179D3
cosocleC9×D5C2×C179
LCSG ▷ C5×C9
UCSC1 ◁ C179

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8055

Conjugacy classes & character table

3759 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 14);