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C3×(C1039⋊C3)⋊C4 #49153404

order37404
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C1039⋊C3)⋊C4
unambiguous semidirect product(C1039⋊C3)⋊(C3×C4)
unambiguous semidirect productDic1039⋊C32
unambiguous semidirect product(C3×Dic1039)⋊C3

Splittings

derived, SylowC1039 ⋊ C32×C4
HallC3×C1039⋊C3 ⋊ C4
HallDic1039 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D1039⋊C3
commutator, hypocenterC1039C32×C4
FrattiniC2C3×D1039⋊C3
Fitting, socleC2×C3×C1039C2×C3
prime radicalC2×C3×C1039⋊C3C2
cosocleC2×C1039C2×C32
LCSG ▷ C1039
UCSC1 ◁ C2×C3

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12468

Conjugacy classes & character table

1074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37404, 17);