Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7542 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 181 points:
(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)(54,56,61,74)(55,62,68,98)(57,76,81,122)(58,82,85,71)(59,87,89,120)(60,91,92,150)(63,100,105,116)(64,97,67,94)(65,109,111,114)(66,112,113,159)(69,75,119,135)(70,79,124,145)(72,77,127,88)(73,129,130,84)(78,141,143,136)(80,147,148,181)(83,152,153,156)(86,95,101,161)(90,96,107,162)(93,99,121,164)(102,168,104,165)(103,171,172,177)(106,173,110,174)(108,149,140,125)(115,134,118,131)(117,146,175,179)(123,163,176,180)(126,132,167,170)(128,133,166,169)(137,139,157,144)(138,178,155,142)(151,160,154,158);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,55,58,64,61,68,85,67)(56,69,71,115,74,119,82,118)(57,75,78,131,81,135,143,134)(59,86,83,151,89,101,153,154)(60,90,84,66,92,107,129,113)(62,93,94,70,98,121,97,124)(63,99,102,145,105,164,104,79)(65,108,106,77,111,140,110,88)(72,126,125,171,127,167,149,177)(73,128,91,117,130,166,150,175)(76,109,136,174,122,114,141,173)(80,146,142,133,148,179,178,169)(87,116,156,168,120,100,152,165)(95,147,158,155,161,181,160,138)(96,123,159,157,162,176,112,137)(103,139,170,180,172,144,132,163)Polycyclic presentation:
2^8,53|a^2=d,b^2=h,c^2=efh,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,c^b=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh,i^b=i^521034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57460);