Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×(C2×#87938)⋊Q8 |
| unambiguous semidirect product | D101⋊#391 |
| Fitting | C22×Q8×C101 ⋊ C4 |
| Sylow | C101 ⋊ C2×#391 |
928 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,12,22,36,54,38,24,14,4,8,16,28,42,58,72,60,44,26,10,18,30,46,64,76,86,78,62,40,20,32,48,66,80,90,96,88,74,56,34,50,68,82,92,98,100,94,84,70,52,51,69,83,93,99,101,97,87,73,55,33,49,67,81,91,95,89,77,59,37,19,31,47,65,79,85,75,63,43,23,9,17,29,45,61,71,57,41,27,13,3,7,15,25,39,53,35,21,11,5)(108,110,111,115)(109,112,113,114);(2,4,5,3)(6,10,11,9)(7,8,14,13)(12,20,21,19)(15,18,24,23)(16,26,27,17)(22,34,35,33)(25,32,38,37)(28,40,41,31)(29,30,44,43)(36,52,53,51)(39,50,54,55)(42,56,57,49)(45,48,60,59)(46,62,63,47)(58,70,71,69)(61,68,72,73)(64,74,75,67)(65,66,78,77)(76,84,85,83)(79,82,86,87)(80,88,89,81)(90,94,95,93)(91,92,96,97)(98,100,101,99)(105,107);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,54,50)(42,49,57,56)(45,59,60,48)(46,47,63,62)(58,69,71,70)(61,73,72,68)(64,67,75,74)(65,77,78,66)(76,83,85,84)(79,87,86,82)(80,81,89,88)(90,93,95,94)(91,97,96,92)(98,99,101,100)(104,105,106,107)(108,109,111,113)(110,114,115,112);(102,103)556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20968);