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C372 #13063113
Aliases
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 74 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)
Conjugacy classes & character table
1369 conjugacy classes. The character table is too large to display.
Relationships
| center of | D5×C372, A4×C372, D7×C372, … |
| derived subgroup of | C37⋊D37, #16861551, #16861552, … |
| Fitting subgroup of | C37×D37, C37⋊D37, C37×C37⋊C3, … |
| socle of | C37×D37, C37⋊D37, C37×C37⋊C3, … |
| maximal subgroup of | C37×D37, C37⋊D37, C2×C372, … |
| maximal normal subgroup of | C37×D37, C37⋊D37, C2×C372, … |
| maximal quotient of | C2×C372, C3×C372, C11×C372, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1369, 2);
Finite Group Databasebeta