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C2×C3⋊(D151⋊C3) #19129557

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

Aliases

direct productC2×C3⋊(D151⋊C3)
unambiguous semidirect product(C2×C3)⋊(D151⋊C3)
unambiguous semidirect product(C2×C151⋊C3)⋊D3
unambiguous semidirect product(C2×D453)⋊C3

Splittings

Fitting, socleC2×C3×C151 ⋊ C2×C3
derivedC3×C151 ⋊ C22×C3
HallC3×C151⋊C3 ⋊ C22
SylowC151 ⋊ C2×C3×D3

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(D151⋊C3)
commutator, hypocenterC3×C151C22×C3
FrattiniC1G
Fitting, socleC2×C3×C151C2×C3
LCSG ▷ C3×C151
UCSC1 ◁ C2

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3⋊((D151⋊C3)⋊C5), D5×C3⋊(D151⋊C3), C2×C5×C3⋊(D151⋊C3), …
maximal normal subgroup ofC2×C3⋊((D151⋊C3)⋊C5), C2×C5×C3⋊(D151⋊C3), C2×C7×C3⋊(D151⋊C3)
maximal quotient ofD5×C3⋊(D151⋊C3), C2×C5×C3⋊(D151⋊C3), C2×C3⋊(C5⋊(D151⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5436, 30);