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C2×C3×D429 #19104247

order5148
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D429
unambiguous semidirect product(C2×C3)⋊(C3×D143)
unambiguous semidirect product(C2×C11)⋊(C3×D39)

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derivedC3×C11×C13 ⋊ C22×C3
HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ C2×C3×D3
HallC32×C13 ⋊ C2×D11
HallC32×C11 ⋊ C2×D13
SylowC13 ⋊ C2×C3×D33
SylowC11 ⋊ C2×C3×D39
SylowC32 ⋊ C2×D143

Subgroups

subgroupG/H
center, hypercenterC2×C3D429
commutator, hypocenterC3×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C3⋊(C13⋊AGL(1,𝔽11)), C3×D5×D429, C2×C3×C5×D429, …
maximal normal subgroup ofC2×C3×C3⋊(C13⋊AGL(1,𝔽11)), C2×C3×C5×D429, C2×C3×C7×D429
maximal quotient ofC3×D5×D429, C2×C3×C5×D429, C2×C3×D2145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 123);