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C29×#2678 #16816392

order3712
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C29 · Schur multiplier (H2) = C24×C4

Aliases

direct productC29×#2678

Subgroups

subgroupG/H
center, socleC23×C29C24
commutator, Frattini, cosocleC23C24×C29
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C29 ◁ G

802 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)(30,31,32,33)(38,39)(40,44)(41,42)(43,45);(35,37)(39,42)(40,45);(30,31)(32,33)(34,35)(36,37)(38,39)(40,43)(41,42)(44,45);(30,31)(32,33)(38,40)(39,43)(41,45)(42,44)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#36703, C29×#36713, C29×#36714, …
maximal normal subgroup ofC29×#36703, C29×#36713, C29×#36714, …
maximal quotient ofC29×#14357, C29×#14358, C29×#14359, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1410);