Finite Group Databasebeta

← Prev (#14579058) Next (#14579060) →

#137×C79 #14579059

order2528
nilpotency class3
isoclinismisoclinic class of AGL(1,ℤ/8)
automorphism?
homologyAbelianization (H1) = C23×C79 · Schur multiplier (H2) = C22

Aliases

direct product#137×C79

Subgroups

subgroupG/H
center, socleC2×C79C2×D4
commutator, Frattini, cosocleC4C23×C79
prime radical#41×C79C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C79 ◁ C2×C4×C79 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 1264

A minimal faithful permutation representation — 3 generators on 95 points:

(1,2)(3,9)(4,12)(5,7)(6,10)(8,14)(11,16)(13,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,3,5,11)(2,6,7,15)(4,13,14,10)(8,16,12,9);(2,7)(6,15)(8,12)(9,16)

Conjugacy classes & character table

869 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#455×C79, #456×C79, #471×C79, …
maximal normal subgroup of#455×C79, #456×C79, #471×C79, …
maximal quotient of#417×C79, #419×C79, #428×C79, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2528, 44);