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C29×#3194 #16816908

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

Aliases

direct productC29×#3194

Subgroups

subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

466 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)(40,43)(41,44)(42,45);(30,32)(31,34)(33,37)(35,36)(38,40,42,41)(39,43,45,44);(32,37)(34,36)(39,44)(40,41)(43,45);(31,35)(34,36)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#9332, C29×#18322, C29×#18330, …
maximal normal subgroup ofC29×#9332, C29×#18322, C29×#18330, …
maximal quotient ofC29×#21767, C29×#21769, C29×#21944, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1926);