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C3×(C151⋊C3)⋊C4 #19129544

order5436
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C151⋊C3)⋊C4
unambiguous semidirect product(C151⋊C3)⋊(C3×C4)
unambiguous semidirect productDic151⋊C32
unambiguous semidirect product(C3×Dic151)⋊C3

Splittings

derived, SylowC151 ⋊ C32×C4
HallC3×C151⋊C3 ⋊ C4
HallDic151 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D151⋊C3
commutator, hypocenterC151C32×C4
FrattiniC2C3×D151⋊C3
Fitting, socleC2×C3×C151C2×C3
LCSG ▷ C151
UCSC1 ◁ C2×C3

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C151⋊C3)⋊C4)⋊C5, C3×C5×(C151⋊C3)⋊C4, C3×(C151⋊C3)⋊Dic5, …
maximal normal subgroup ofC3×((C151⋊C3)⋊C4)⋊C5, C3×C5×(C151⋊C3)⋊C4, C3×C7×(C151⋊C3)⋊C4
maximal quotient ofC3×C5×(C151⋊C3)⋊C4, C3×(C151⋊C3)⋊Dic5, C3×(C151⋊C3)⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5436, 17);