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#27369478

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 101 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)(54,57,59,58)(55,61,62,67)(56,64,66,65)(60,63,68,69)(72,81)(76,90)(80,95)(82,97)(89,100)(91,98)(94,101)(96,99);(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)(70,73,75,85)(71,77,79,92)(72,80,81,95)(74,87,88,84)(76,89,90,100)(78,93,86,83)(82,99,97,96)(91,101,98,94);(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)(54,56,58,65,59,66,57,64)(55,60,61,63,62,68,67,69)(70,72)(71,76)(73,80)(74,82)(75,81)(77,89)(78,91)(79,90)(83,94)(84,96)(85,95)(86,98)(87,99)(88,97)(92,100)(93,101);(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)(54,55,59,62)(56,63,66,69)(57,61,58,67)(60,64,68,65)(70,71,75,79)(72,76,81,90)(73,83,85,93)(74,86,88,78)(77,87,92,84)(80,94,95,101)(82,98,97,91)(89,99,100,96)

Polycyclic presentation:

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

Conjugacy classes & character table

1037 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 154954);