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C3×C5×(C67⋊C3)⋊C4 #27130372

order12060
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×(C67⋊C3)⋊C4
unambiguous semidirect product(C67⋊C3)⋊(C3×C4×C5)
unambiguous semidirect productDic67⋊(C32×C5)
unambiguous semidirect product(C3×Dic67)⋊(C3×C5)
unambiguous semidirect product(C5×Dic67)⋊C32
unambiguous semidirect product(C3×C5×Dic67)⋊C3

Splittings

derived, SylowC67 ⋊ C32×C4×C5
HallC3×C5×C67⋊C3 ⋊ C4
HallC5×Dic67 ⋊ C32
HallC3×C67⋊C3 ⋊ C4×C5
HallC5×C67 ⋊ C32×C4
HallDic67 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D67⋊C3
commutator, hypocenterC67C32×C4×C5
FrattiniC2C3×C5×D67⋊C3
Fitting, socleC2×C3×C5×C67C2×C3
prime radicalC2×C3×C5×C67⋊C3C2
cosocleC2×C67C2×C32×C5
LCSG ▷ C67
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

510 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12060, 42);