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C2×C7⋊(C23⋊AGL(1,𝔽11)) #47978430

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

Aliases

direct productC2×C7⋊(C23⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C7)⋊(C23⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C23)⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D161
unambiguous semidirect product(C2×D1771)⋊C5

Splittings

Fitting, socleC2×C7×C11×C23 ⋊ C2×C5
derived, HallC7×C11×C23 ⋊ C22×C5
HallC7×C23×C11⋊C5 ⋊ C22
HallC2×D1771 ⋊ 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 ⋊ C2×D161
SylowC23 ⋊ C2×C7⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D161
SylowC7 ⋊ C2×C23⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C7⋊(C23⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC7×C11×C23C22×C5
FrattiniC1G
Fitting, socleC2×C7×C11×C23C2×C5
LCSG ▷ C7×C11×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 3542

A minimal faithful permutation representation — 2 generators on 43 points:

(4,5)(6,7)(8,9)(11,15,16,14,19,12,13,20,17,18)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43);(1,2)(3,4,6,8,9,7,5)(10,11,14,19,13,16,20,15,18,17,12)(21,22,24,26,28,30,32,34,36,38,40,42,43,41,39,37,35,33,31,29,27,25,23)

Conjugacy classes & character table

1142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 64);