Finite Group Databasebeta

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AGL(1,𝔽11)×D111 #37567529

order24420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽11)×D111
unambiguous semidirect productD11⋊(C5×D111)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊D37
unambiguous semidirect product(C37×AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D11×D111)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C37 ⋊ C22×C5
HallC3×C37×C11⋊C5 ⋊ C22
HallD11×D111 ⋊ C5
HallC37×C11⋊C5 ⋊ C2×D3
HallC11×C37 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D37
HallC3×C37 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D111
SylowC37 ⋊ D3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D37
SylowC11 ⋊ C2×C5×D111
SylowC3 ⋊ D37×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C37C22×C5
LCSG ▷ C3×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1221

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 50);