Finite Group Databasebeta

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C3×Dic3×C61⋊C5 #24926728

order10980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C61⋊C5
unambiguous semidirect productC3⋊(C3×C4×C61⋊C5)
unambiguous semidirect product(C3×Dic3×C61)⋊C5

Splittings

derivedC3×C61 ⋊ C3×C4×C5
HallC32×C61⋊C5 ⋊ C4
HallC3×Dic3×C61 ⋊ C5
HallC32×C61 ⋊ C4×C5
SylowC61 ⋊ C3×C5×Dic3
SylowC32 ⋊ C4×C61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C61⋊C5
commutator, hypocenterC3×C61C3×C4×C5
FrattiniC2C3×D3×C61⋊C5
Fitting, socleC2×C32×C61C2×C5
prime radicalC2×C32×C61⋊C5C2
cosocleC2×C3×C61C2×C3×C5
LCSG ▷ C3×C61
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

306 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 78);