Finite Group Databasebeta

← Prev (#16816964) Next (#16816966) →

C29×#3251 #16816965

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

Aliases

direct productC29×#3251

Subgroups

subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1856

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#18594, C29×#18596, C29×#18606, …
maximal normal subgroup ofC29×#18594, C29×#18596, C29×#18606, …
maximal quotient ofC29×#21890, C29×#21891, C29×#21963, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1983);