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C29×#1655 #16815369

order3712
nilpotency class3
isoclinismisoclinic class of #1655
automorphism?
homologyAbelianization (H1) = C23×C29 · Schur multiplier (H2) = C2×C4

Aliases

direct productC29×#1655

Subgroups

subgroupG/H
center, socleC22×C29#120
commutator, Frattini, cosocleC42C23×C29
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(31,35)(32,33)(36,37)(39,42)(40,44)(43,45);(30,31)(32,37)(33,35)(34,36)(38,39)(40,45)(41,43)(42,44);(30,31)(32,35)(33,37)(34,36)(40,44)(42,45)

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#13677, C2×C29×#1655, C29×#18984, …
maximal normal subgroup ofC29×#13677, C2×C29×#1655, C29×#18984, …
maximal quotient ofC29×#7734, C29×#7742, C29×#7745, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 387);