Finite Group Databasebeta

C29×M128 #16815142

order3712
nilpotency class2
isoclinismisoclinic class of D4
automorphism?
homologyAbelianization (H1) = C2×C29×C32 · Schur multiplier (H2) = C1

Aliases

direct productC29×M128

Subgroups

subgroupG/H
centerC29×C32C22
commutatorC2C2×C29×C32
Frattini, cosocleC32C22×C29
socleC2×C29C2×C32
prime radicalC22×C29C32
LCSG ▷ C2 ▷ C1
UCSC1 ◁ 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);(31,63)(33,65)(35,67)(37,69)(39,71)(41,73)(43,75)(45,77)(47,79)(49,81)(51,83)(53,85)(55,87)(57,89)(59,91)(61,93)

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC29×#7511, C29×#7513, C29×#7514, …
maximal normal subgroup ofC29×#7511, C29×#7513, C29×#7514, …
maximal quotient ofC29×#7510, C29×C22⋊C64, C29×C4⋊C64, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 160);