Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #575×C103 ⋊ C2 |
| Sylow | C103 ⋊ #3067 |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 135 |
| transitive degree | μt(G) = 3296 |
A minimal faithful permutation representation — 4 generators on 135 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(104,108,110,109)(105,113,115,114)(106,118,120,119)(107,122,123,124)(111,126,127,116)(112,128,129,121)(117,132,133,134)(125,135,131,130);(104,107)(105,112)(106,117)(108,122)(109,124)(110,123)(111,125)(113,128)(114,121)(115,129)(116,130)(118,132)(119,134)(120,133)(126,135)(127,131);(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)(102,103)(104,106,108,118,110,120,109,119)(105,111,114,116,115,127,113,126)(107,117,122,132,123,133,124,134)(112,125,121,130,129,131,128,135);(104,105)(106,116)(107,121)(108,113)(109,114)(110,115)(111,118)(112,122)(117,131)(119,127)(120,126)(123,128)(124,129)(125,133)(130,132)(134,135)Polycyclic presentation:
2^7,103|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^102,f^c=fg1154 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 14227);