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Cayley diagramAliases
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 169 points:
(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169)
Conjugacy classes & character table
334 conjugacy classes. The character table is too large to display.
Relationships
| center of | D4×C167, Q8×C167, Dic3×C167, … |
| derived subgroup of | C22⋊D167, D668, Dic334, … |
| Fitting subgroup of | Dic167, C2×D167 |
| socle of | Dic167, C4×C167, C2×D167, … |
| maximal subgroup of | Dic167, C4×C167, C2×D167, … |
| maximal normal subgroup of | Dic167, C4×C167, C2×D167, … |
| maximal quotient of | C4×C167, C22×C167, D3×C167, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(334, 2);
Finite Group Databasebeta