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#27496219

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

582 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 93 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(62,65,66,73)(63,69,67,75)(64,70,71,72)(68,76,74,77)(79,86)(80,89)(85,87)(88,90);(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)(55,59)(58,61)(62,64,66,71)(63,68,67,74)(65,72,73,70)(69,77,75,76)(79,85)(80,88)(81,82)(86,87)(89,90)(91,92);(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)(54,56,57,60)(55,58,59,61)(63,67)(68,74)(69,75)(76,77)(78,80,81,88,83,89,82,90)(79,84,87,91,86,93,85,92);(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)(56,58)(57,59)(60,61)(62,63,66,67)(64,68,71,74)(65,69,73,75)(70,76,72,77)(78,79,81,87,83,86,82,85)(80,84,88,91,89,93,90,92)

Polycyclic presentation:

2^8,53|a^2=egh,b^2=f,c^2=e,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^52,c^b=cg,d^b=dh,i^b=i^52,d^c=de,f^c=fh,g^c=gh,i^c=i^52

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 281695);