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C2×C29×#472 #16816779

order3712
nilpotency class3
isoclinismisoclinic class of #471
automorphism?
homologyAbelianization (H1) = C24×C29 · Schur multiplier (H2) = C25

Aliases

direct productC2×C29×#472

Subgroups

subgroupG/H
center, socleC22×C29#121
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 928

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(4,8)(5,12)(6,9)(11,16)(13,14)(15,17);(3,4,9,16,7,11,6,8)(5,10,12,17,14,18,13,15);(3,5)(4,10)(6,13)(7,14)(8,15)(9,12)(11,18)(16,17)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#12996, C29×#13007, C29×#13068, …
maximal normal subgroup ofC29×#12996, C29×#13007, C29×#13068, …
maximal quotient ofC2×C29×#1667, C2×C29×#1675, C2×C29×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1797);