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C3×(C211⋊C3)⋊Dic5 #49183992

order37980
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C211⋊C3)⋊Dic5
unambiguous semidirect product(C211⋊C3)⋊(C3×Dic5)
unambiguous semidirect productDic1055⋊C32
unambiguous semidirect product(C3×Dic1055)⋊C3

Splittings

derived, HallC5×C211 ⋊ C32×C4
HallC3×C5×C211⋊C3 ⋊ C4
HallDic1055 ⋊ C32
HallC3×C211⋊C3 ⋊ Dic5
SylowC211 ⋊ C32×Dic5
SylowC5 ⋊ C3×(C211⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D211⋊C3)
commutator, hypocenterC5×C211C32×C4
FrattiniC2C3×C5⋊(D211⋊C3)
Fitting, socleC2×C3×C5×C211C2×C3
prime radicalC2×C3×C5×C211⋊C3C2
cosocleC2×C5×C211C2×C32
LCSG ▷ C5×C211
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12660

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37980, 67);