Finite Group Databasebeta

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C101×C9⋊AGL(1,𝔽5) #32911398

order18180
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C101 · Schur multiplier (H2) = C1

Aliases

direct productC101×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C101)

Splittings

Fitting, HallC5×C9×C101 ⋊ C4
derived, HallC5×C9 ⋊ C4×C101
HallC9×C101 ⋊ AGL(1,𝔽5)
HallC5×C101 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C101
SylowC5 ⋊ Dic9×C101

Subgroups

subgroupG/H
center, hypercenterC101C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C101
FrattiniC3ΓL(1,𝔽16)×C101
FittingC5×C9×C101C4
socleC3×C5×C101Dic3
prime radicalC3×D5×C101D3
cosocleC9×D5C2×C101
LCSG ▷ C5×C9
UCSC1 ◁ C101

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4545

Conjugacy classes & character table

2121 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 31);