Finite Group Databasebeta

C109×#1384 #28358638

order13952
nilpotency class4
isoclinismisoclinic class of #365
automorphism?
homologyAbelianization (H1) = C42×C109 · Schur multiplier (H2) = C2×C4

Aliases

direct productC109×#1384

Subgroups

subgroupG/H
centerC4×C109#106
commutatorC8C42×C109
Frattini, cosocleC22×C8C22×C109
socleC2×C109#340
prime radicalC23×C109D8
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C109 ◁ C22×C4×C109 ◁ C22×C8×C109 ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 141
transitive degreeμt(G) = 3488

A minimal faithful permutation representation — 2 generators on 141 points:

(1,2)(3,13,15,27)(4,10)(5,20)(6,22)(7,12)(8,14,23,28)(9,18)(11,21)(16,31,29,25)(17,32,30,24)(19,26)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3,5,16,21,30,19,28,7,15,18,29,6,17,4,14)(2,8,10,24,22,31,9,13,12,23,26,32,11,25,20,27)

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC109×#7422, C109×#7423, C2×C109×#1384, …
maximal normal subgroup ofC109×#7422, C109×#7423, C2×C109×#1384, …
maximal quotient ofC109×#7157, C109×#7174, C109×#7218, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 116);