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Cayley diagramAliases
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 91 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)
Conjugacy classes & character table
178 conjugacy classes — view the full character table.
Relationships
| center of | D4×C89, Q8×C89, Dic3×C89, … |
| derived subgroup of | Dic178, D356, C22⋊D89, … |
| Frattini subgroup of | C4×C7921, Dic7921, Dic15842, … |
| Fitting subgroup of | Dic89, C2×D89, #10623496, … |
| socle of | Dic89, C4×C89, C2×D89, … |
| maximal subgroup of | Dic89, C4×C89, C2×D89, … |
| maximal normal subgroup of | Dic89, C4×C89, C2×D89, … |
| maximal quotient of | C4×C89, C22×C89, D3×C89, … |
| automorphism group of | C179, C2×C179 |
| outer automorphism group of | C179, C2×C179 |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(178, 2);
Finite Group Databasebeta