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C3×(Dic61⋊C3)⋊C5 #24926722

order10980
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×(Dic61⋊C3)⋊C5
unambiguous semidirect product(Dic61⋊C3)⋊(C3×C5)
unambiguous semidirect product(Dic61⋊C5)⋊C32
unambiguous semidirect product(C3×Dic61⋊C3)⋊C5
unambiguous semidirect product(C3×Dic61⋊C5)⋊C3

Splittings

derived, SylowC61 ⋊ C32×C4×C5
HallC3×(C61⋊C3)⋊C5 ⋊ C4
HallC3×Dic61⋊C3 ⋊ C5
HallDic61⋊C5 ⋊ C32
HallC3×C61⋊C3 ⋊ C4×C5
HallC61⋊C5 ⋊ C32×C4
HallDic61 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3(D61⋊C3)⋊C5
commutator, hypocenterC61C32×C4×C5
FrattiniC2C3×(D61⋊C3)⋊C5
Fitting, socleC2×C3×C61C2×C3×C5
prime radicalC2×C3×(C61⋊C3)⋊C5C2
cosocleC2×C61C2×C32×C5
LCSG ▷ C61
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 72);