Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #405×C101 ⋊ C2 |
| Sylow | C101 ⋊ #3156 |
532 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 4 generators on 137 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(109,121)(113,127)(118,132)(122,131)(125,136)(128,134)(129,137)(133,135);(102,103,104,105)(106,109)(107,113)(108,118)(110,122)(111,121)(112,125)(114,128)(115,127)(116,129)(117,131)(119,133)(120,132)(123,134)(124,135)(126,136)(130,137);(106,108,117,124,111,120,110,119)(107,112,123,130,115,126,114,116)(109,118,131,135,121,132,122,133)(113,125,134,137,127,136,128,129);(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)(103,105)(106,107,111,115)(108,116,120,130)(109,113,121,127)(110,123,117,114)(112,124,126,119)(118,129,132,137)(122,134,131,128)(125,135,136,133)Polycyclic presentation:
2^7,101|a^2=g,b^2=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^100,d^c=dg2032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 15004);