Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#20266102 |
| Fitting | C2×C16×C101 ⋊ C4 |
| Sylow | C101 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 3 generators on 119 points:
(1,2,5,10,19,32,49,35,22,13,6,11,20,33,50,66,69,54,39,26,15,24,37,52,67,81,84,73,58,43,28,41,56,71,82,92,95,88,77,62,45,60,75,86,93,99,101,97,90,79,64,47,65,80,91,98,100,94,83,68,51,30,46,63,78,89,96,87,72,53,34,17,29,44,59,74,85,76,57,38,21,8,16,27,40,55,70,61,42,25,12,3,7,14,23,36,48,31,18,9,4)(104,105,106,109,107,111,112,116,108,110,113,115,114,117,119,118);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,64)(36,51,49,60)(40,53,54,56)(44,57,58,52)(46,61,62,50)(55,68,69,75)(59,72,73,71)(63,76,77,67)(65,70,79,66)(74,83,84,86)(78,87,88,82)(80,85,90,81)(89,94,95,93)(91,96,97,92)(98,100,101,99)(105,109,110,115)(106,112)(107,114)(111,118,117,116)(113,119);(102,103)832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20855);