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C32×C11×C29⋊C7 #34117138

order20097
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C32×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×C29⋊C7
unambiguous semidirect productC29⋊(C32×C7×C11)
unambiguous semidirect product(C3×C29)⋊(C3×C7×C11)
unambiguous semidirect product(C32×C29)⋊(C7×C11)
unambiguous semidirect product(C11×C29)⋊(C32×C7)
unambiguous semidirect product(C3×C11×C29)⋊(C3×C7)
unambiguous semidirect product(C32×C11×C29)⋊C7

Splittings

Fitting, socle, HallC32×C11×C29 ⋊ C7
derived, SylowC29 ⋊ C32×C7×C11
HallC11×C29 ⋊ C32×C7
HallC32×C29 ⋊ C7×C11

Subgroups

subgroupG/H
center, hypercenterC32×C11C29⋊C7
commutator, cosocle, hypocenterC29C32×C7×C11
FrattiniC1G
Fitting, socleC32×C11×C29C7
LCSG ▷ C29
UCSC1 ◁ C32×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 2871

A minimal faithful permutation representation — 2 generators on 46 points:

(2,3,5,8,9,15,20)(4,7,12,19,27,6,10)(11,18,16,24,28,14,17)(13,21,23,26,25,22,29)(30,31,32,33,34,35,36,37,38,39,40)(44,45,46);(1,2,4,7,13,22,21,8,14,23,24,10,17,25,19,28,3,6,11,12,20,27,29,15,5,9,16,18,26)(41,42,43)

Conjugacy classes & character table

1089 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20097, 5);