Finite Group Databasebeta

← Prev (#16815435) Next (#16815437) →

C29×#1722 #16815436

order3712
nilpotency class3
isoclinismisoclinic class of #1714
automorphism?
homologyAbelianization (H1) = C23×C29 · Schur multiplier (H2) = C2×C4

Aliases

direct productC29×#1722

Subgroups

subgroupG/H
center, socleC22×C29#127
commutator, Frattini, cosocleC42C23×C29
prime radicalC29×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 1856

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)(31,34)(32,35)(36,37)(38,39,42,45)(40,46,47,53)(41,49,50,44)(43,51,52,48);(38,40,41,48,42,47,50,51)(39,43,44,46,45,52,49,53);(30,31,35,37,33,36,32,34)(40,47)(43,52)(46,53)(48,51)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#7528, C29×#12315, C2×C29×#1722, …
maximal normal subgroup ofC29×#7528, C29×#12315, C2×C29×#1722, …
maximal quotient ofC29×#8820, C29×#9830, C29×#9831, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 454);