Finite Group Databasebeta

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D5×C3⋊(C11⋊AGL(1,𝔽7)) #28357606

order13860
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×C3⋊(C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C3×D5)⋊(C11⋊AGL(1,𝔽7))
unambiguous semidirect product(D5×C11)⋊(C3⋊AGL(1,𝔽7))
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊D33
unambiguous semidirect product(D5×D231)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C7×C11 ⋊ C22×C3
HallC3×C5×C11×ΓL(1,𝔽8) ⋊ C22
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×C7×C11 ⋊ C2×C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×D11
HallC7×C11 ⋊ C3×D3×D5
HallC3×ΓL(1,𝔽8) ⋊ D5×D11
HallC5×C11 ⋊ C2×C3⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D33
SylowC11 ⋊ D5×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D5×D33
SylowC5 ⋊ C2×C3⋊(C11⋊AGL(1,𝔽7))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C22×C3
LCSG ▷ C3×C5×C7×C11
UCSC1

176 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 273);