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D7×D13×C11⋊C5 #34093459

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

Aliases

direct productD7×D13×C11⋊C5
unambiguous semidirect product(C13×D7)⋊(C2×C11⋊C5)
unambiguous semidirect product(C7×D13)⋊(C2×C11⋊C5)
unambiguous semidirect productD91⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D7×D13)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C5
HallC7×C13×C11⋊C5 ⋊ C22
HallC11×D7×D13 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D7
HallC7×C13 ⋊ C22×C11⋊C5
HallC7×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×D7×C11⋊C5
SylowC11 ⋊ C5×D7×D13
SylowC7 ⋊ C2×D13×C11⋊C5

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 36);