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C3×Dic5×C211⋊C3 #49183993

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

Aliases

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

Splittings

derived, HallC5×C211 ⋊ C32×C4
HallC3×C5×C211⋊C3 ⋊ C4
HallDic5×C211 ⋊ C32
SylowC211 ⋊ C32×Dic5
SylowC5 ⋊ C3×C4×C211⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C211⋊C3
commutator, hypocenterC5×C211C32×C4
FrattiniC2C3×D5×C211⋊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

1752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37980, 68);