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C29×#1822 #16815536

order3712
nilpotency class3
isoclinismisoclinic class of #1462
automorphism?
homologyAbelianization (H1) = C22×C4×C29 · Schur multiplier (H2) = C23

Aliases

direct productC29×#1822

Subgroups

subgroupG/H
center, socleC22×C29C2×C22⋊C4
commutatorC23C22×C4×C29
Frattini, cosocleC22×C4C23×C29
prime radicalC24×C29C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 928

A minimal faithful permutation representation — 3 generators on 53 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)(32,35)(33,34)(36,37)(38,39,41,45,42,44,48,51)(40,43,46,50,47,49,52,53);(31,34)(35,37)(38,40,42,47)(39,43,44,49)(41,46,48,52)(45,50,51,53);(30,32,33,36)(31,35,34,37)(39,44)(41,48)(43,49)(46,52)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#7216, C29×#7350, C29×#7351, …
maximal normal subgroup ofC29×#7216, C29×#7350, C29×#7351, …
maximal quotient ofC29×#8699, C29×#8700, C29×#8702, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 554);