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Aliases
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 128 points:
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)
Conjugacy classes & character table
847 conjugacy classes. The character table is too large to display.
Relationships
| center of | C7×D9×C121, C7×C3⋊D3×C121, C7×AGL(1,𝔽5)×C121, … |
| derived subgroup of | D847, Dic847, D7×D121, … |
| Fitting subgroup of | D7×C121, C7×D121, D847, … |
| maximal subgroup of | D7×C121, C7×D121, D847, … |
| maximal normal subgroup of | D7×C121, C7×D121, D847, … |
| maximal quotient of | C2×C7×C121, C3×C7×C121, C5×C7×C121, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(847, 1);
Finite Group Databasebeta