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C11×D13×D35 #34093504

order20020
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D13×D35
unambiguous semidirect product(C5×D13)⋊(C11×D7)
unambiguous semidirect product(C7×D13)⋊(D5×C11)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C22
derived, HallC5×C7×C13 ⋊ C22×C11
HallC7×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D35
HallC7×C13 ⋊ C2×D5×C11
HallC7×C11 ⋊ D5×D13
HallC5×C13 ⋊ C2×C11×D7
HallC5×C11 ⋊ D7×D13
HallC5×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C11×D35
SylowC7 ⋊ D5×C11×D13
SylowC5 ⋊ C11×D7×D13

Subgroups

subgroupG/H
center, hypercenterC11D13×D35
commutator, cosocle, hypocenterC5×C7×C13C22×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C13C22
LCSG ▷ C5×C7×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 5005

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 81);