Finite Group Databasebeta

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C2×C3×D151⋊C3 #19129556

order5436
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D151⋊C3
unambiguous semidirect productD151⋊(C2×C32)
unambiguous semidirect product(C151⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D151)⋊C32
unambiguous semidirect product(C2×C151⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D151)⋊C3

Splittings

Fitting, socleC2×C3×C151 ⋊ C2×C3
derived, SylowC151 ⋊ C22×C32
HallC3×C151⋊C3 ⋊ C22
HallC2×D151 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D151⋊C3
commutator, hypocenterC151C22×C32
FrattiniC1G
Fitting, socleC2×C3×C151C2×C3
LCSG ▷ C151
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×(D151⋊C3)⋊C5, C3×D5×D151⋊C3, C2×C3×C5×D151⋊C3, …
maximal normal subgroup ofC2×C3×(D151⋊C3)⋊C5, C2×C3×C5×D151⋊C3, C2×C3×C7×D151⋊C3
maximal quotient ofC3×D5×D151⋊C3, C2×C3×C5×D151⋊C3, C2×C3×C5⋊(D151⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5436, 29);