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C13×C7⋊(Dic11⋊C5) #34093446

order20020
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C7⋊(Dic11⋊C5)
unambiguous semidirect productC7⋊(C13×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C13×Dic7)
unambiguous semidirect productDic77⋊(C5×C13)
unambiguous semidirect product(C13×Dic77)⋊C5

Splittings

derived, HallC7×C11 ⋊ C4×C5×C13
HallC7×C13×C11⋊C5 ⋊ C4
HallC13×Dic77 ⋊ C5
HallC7×C11×C13 ⋊ C4×C5
HallC13×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C4×C13
HallDic77 ⋊ C5×C13
HallC11×C13 ⋊ C5×Dic7
HallC7×C13 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C13×Dic7
SylowC11 ⋊ C5×C13×Dic7
SylowC7 ⋊ C13×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C13C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C5×C13
FrattiniC2C13×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C7×C11×C13C2×C5
prime radicalC2×C7×C13×C11⋊C5C2
cosocleC2×C7×C11C2×C5×C13
LCSG ▷ C7×C11
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 4004

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 23);