Finite Group Databasebeta

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C3×Dic5×C61⋊C3 #24926733

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

Aliases

direct productC3×Dic5×C61⋊C3
unambiguous semidirect product(Dic5×C61)⋊C32
unambiguous semidirect product(C3×Dic5×C61)⋊C3

Splittings

derived, HallC5×C61 ⋊ C32×C4
HallC3×C5×C61⋊C3 ⋊ C4
HallDic5×C61 ⋊ C32
SylowC61 ⋊ C32×Dic5
SylowC5 ⋊ C3×C4×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C61⋊C3
commutator, hypocenterC5×C61C32×C4
FrattiniC2C3×D5×C61⋊C3
Fitting, socleC2×C3×C5×C61C2×C3
prime radicalC2×C3×C5×C61⋊C3C2
cosocleC2×C5×C61C2×C32
LCSG ▷ C5×C61
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

552 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 83);