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C29×#3217 #16816931

order3712
nilpotency class3
isoclinismisoclinic class of #3192
automorphism?
homologyAbelianization (H1) = C24×C29 · Schur multiplier (H2) = C23×C4

Aliases

direct productC29×#3217

Subgroups

subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 928

A minimal faithful permutation representation — 4 generators on 45 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)(30,31)(32,36)(33,35)(34,37)(38,39)(40,42)(41,43)(44,45);(30,32,33,37)(31,34,35,36)(39,42)(43,44);(32,37)(34,36)(39,43)(41,45)(42,44);(31,35)(34,36)(39,42)(43,44)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#9340, C29×#9378, C29×#18335, …
maximal normal subgroup ofC29×#9340, C29×#9378, C29×#18335, …
maximal quotient ofC29×#21810, C29×#21867, C29×#21987, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1949);