Finite Group Databasebeta

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D3×C11×C13×AGL(1,𝔽7) #49114712

order36036
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11×C13×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×D3×C11×C13)
unambiguous semidirect product(D3×D7)⋊(C3×C11×C13)
unambiguous semidirect product(C3×AGL(1,𝔽7))⋊(C2×C11×C13)
unambiguous semidirect product(D3×ΓL(1,𝔽8))⋊(C2×C11×C13)
unambiguous semidirect product(C3⋊AGL(1,𝔽7))⋊(C2×C11×C13)
unambiguous semidirect product(D3×C11×D7)⋊(C3×C13)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C22×C3
derivedC3×C7 ⋊ C22×C3×C11×C13
HallC3×C11×C13×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×C13 ⋊ C2×C3×D3
HallC3×C13×ΓL(1,𝔽8) ⋊ C22×C11
HallC3×C11×ΓL(1,𝔽8) ⋊ C22×C13
HallC7×C13 ⋊ C2×C3×D3×C11
HallC7×C11 ⋊ C2×C3×D3×C13
HallC3×ΓL(1,𝔽8) ⋊ C22×C11×C13
SylowC7 ⋊ C2×C3×D3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC11×C13D3×AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C7C22×C3×C11×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7
UCSC1 ◁ C11×C13

176 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 3003

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 380);