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C29×#595 #14520306

order1972
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×#595

Splittings

Fitting, socle, HallC17×C29 ⋊ C4
derived, SylowC17 ⋊ C4×C29

Subgroups

subgroupG/H
center, hypercenterC29#595
commutator, hypocenterC17C4×C29
FrattiniC1G
Fitting, socleC17×C29C4
prime radicalC29×D17C2
cosocleD17C2×C29
LCSG ▷ C17
UCSC1 ◁ C29

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 493

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

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

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#595×C29⋊C7, C7×C29×#595, C29×C7⋊#595, …
maximal normal subgroup of#595×C29⋊C7, C7×C29×#595, C11×C29×#595, …
maximal quotient ofC7×C29×#595, C29×C7⋊#595, C29×#10597479, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1972, 6);