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D21⋊(C5⋊AGL(1,𝔽11)) #37528467

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

Aliases

unambiguous semidirect productD21⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(D21⋊D55)⋊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 ⋊ D3×D7
HallC3×C7×C11 ⋊ C2×C5×D5
HallC7×C11 ⋊ C5×D3×D5
HallC3×C11 ⋊ C5×D5×D7
HallC3×C7 ⋊ C2×C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D15⋊D7
SylowC7 ⋊ D3×C5⋊AGL(1,𝔽11)
SylowC3 ⋊ D7×C5⋊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 40 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 40 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

Polycyclic presentation:

2^2,5,3,5,7,11|e^a=e^4,f^a=f^6,g^a=g^10,d^b=d^2,f^b=f^6,g^c=g^4

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 278);