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C101×Dic45 #32911375

order18180
isoclinismisoclinic class of D45
automorphism?
homologyAbelianization (H1) = C4×C101 · Schur multiplier (H2) = C1

Aliases

direct productC101×Dic45
unambiguous semidirect productC9⋊(Dic5×C101)

Splittings

derived, HallC5×C9 ⋊ C4×C101
HallC5×C9×C101 ⋊ C4
HallC9×C101 ⋊ Dic5
HallC5×C101 ⋊ Dic9
SylowC9 ⋊ Dic5×C101
SylowC5 ⋊ Dic9×C101

Subgroups

subgroupG/H
center, hypercenterC2×C101D45
commutator, hypocenterC5×C9C4×C101
FrattiniC2×C3D15×C101
FittingC2×C5×C9×C101C2
socle, prime radicalC2×C3×C5×C101D3
cosocleC2×C5×C9C2×C101
LCSG ▷ C5×C9
UCSC1 ◁ C2×C101

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18180

Conjugacy classes & character table

4848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 8);