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D7×C23⋊AGL(1,𝔽11) #47978422

order35420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD7×C23⋊AGL(1,𝔽11)
unambiguous semidirect product(D7×C23)⋊AGL(1,𝔽11)
unambiguous semidirect product(D7×C11⋊C5)⋊D23
unambiguous semidirect product(D7×D253)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C23 ⋊ C22×C5
HallC7×C23×C11⋊C5 ⋊ C22
HallD7×D253 ⋊ C5
HallC23×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C2×D23
HallC11×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C2×AGL(1,𝔽11)
HallC7×C11 ⋊ C2×C5×D23
HallC11⋊C5 ⋊ D7×D23
SylowC23 ⋊ D7×AGL(1,𝔽11)
SylowC11 ⋊ C5×D7×D23
SylowC7 ⋊ C2×C23⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C23C22×C5
LCSG ▷ C7×C11×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 1771

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,4,6,7,5,3)(9,13,14,12,17,10,11,18,15,16)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41);(2,3)(4,5)(6,7)(8,9,12,17,11,14,18,13,16,15,10)(19,20,22,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25,23,21)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 56);