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AGL(1,𝔽11)×D91 #34093455

order20020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽11)×D91
unambiguous semidirect productD11⋊(C5×D91)
unambiguous semidirect product(C7×AGL(1,𝔽11))⋊D13
unambiguous semidirect product(C13×AGL(1,𝔽11))⋊D7
unambiguous semidirect product(D11×D91)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C5
HallC7×C13×C11⋊C5 ⋊ C22
HallD11×D91 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D7
HallC7×C13 ⋊ C2×AGL(1,𝔽11)
HallC7×C11 ⋊ C2×C5×D13
HallC11⋊C5 ⋊ C2×D91
SylowC13 ⋊ D7×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D91
SylowC7 ⋊ D13×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C22×C5
LCSG ▷ C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 1001

A minimal faithful permutation representation — 2 generators on 31 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22,27,23,29)(24,31,30,25,28);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,19,20,18,16)(22,23)(24,26)(25,28)(27,31)(29,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 32);