Finite Group Databasebeta

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C2×C3×C7×D429 #49115019

order36036
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D429
unambiguous semidirect product(C2×C3)⋊(C3×C7×D143)
unambiguous semidirect product(C2×C11)⋊(C3×C7×D39)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derivedC3×C11×C13 ⋊ C22×C3×C7
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C2×C3×D3
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3×D3×C7
HallC32×C13 ⋊ C2×C7×D11
HallC32×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C3×D33
HallC7×C11 ⋊ C2×C3×D39
HallC32×C7 ⋊ C2×D143
SylowC13 ⋊ C2×C3×C7×D33
SylowC11 ⋊ C2×C3×C7×D39
SylowC32 ⋊ C2×C7×D143

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D429
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2×C3×C7

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12012

Conjugacy classes & character table

9072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 687);