Finite Group Databasebeta

C29×SD128 #16815144

order3712
nilpotency class6
isoclinismisoclinic class of D64
automorphism?
homologyAbelianization (H1) = C22×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×SD128

Subgroups

subgroupG/H
center, socleC2×C29D32
commutator, Frattini, cosocleC32C22×C29
prime radicalC29×D32C2
LCSG ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C4×C29 ◁ C8×C29 ◁ C16×C29 ◁ C29×C32 ◁ G

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 1856

A minimal faithful permutation representation — 2 generators on 93 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(31,61)(32,92)(33,59)(34,90)(35,57)(36,88)(37,55)(38,86)(39,53)(40,84)(41,51)(42,82)(43,49)(44,80)(45,47)(46,78)(48,76)(50,74)(52,72)(54,70)(56,68)(58,66)(60,64)(63,93)(65,91)(67,89)(69,87)(71,85)(73,83)(75,81)(77,79)

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C29×SD128, C29×#13741, C29×#13742, …
maximal normal subgroup ofC2×C29×SD128, C29×#13741, C29×#13742, …
maximal quotient ofC29×#7537, C29×#7538, C29×#7546, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 162);