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D5×C3⋊(C7⋊AGL(1,𝔽11)) #37528458

order23100
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD5×C3⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect product(C3×D5)⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect product(C7×D5)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(D5×C11⋊C5)⋊D21
unambiguous semidirect product(D5×D231)⋊C5

Splittings

Fitting, socle, derivedC3×C5×C7×C11 ⋊ C22×C5
HallC3×C5×C7×C11⋊C5 ⋊ C22
HallC5×C7×C11⋊C5 ⋊ C2×D3
HallC3×C5×C11⋊C5 ⋊ C2×D7
HallC5×C11⋊C5 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×C5×D5
HallC7×C11 ⋊ C5×D3×D5
HallC3×C11 ⋊ C5×D5×D7
HallC3×C7 ⋊ D5×AGL(1,𝔽11)
SylowC11 ⋊ C5×D5×D21
SylowC7 ⋊ D5×C3⋊AGL(1,𝔽11)
SylowC3 ⋊ D5×C7⋊AGL(1,𝔽11)

Subgroups

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

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

normal subgroups only

This group has 192 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 269);