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#27304657

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

186 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 117 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)(54,57,59,76,60,69,81,100,58,75,78,106,79,87,109,113,61,77,82,108,83,92,111,115,80,107,91,114,110,62,85,86)(55,63,65,56,66,71,95,72,67,89,96,73,98,102,116,104,68,90,97,74,99,103,117,105,64,88,93,70,94,84,112,101);(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)(54,56)(55,62)(57,66)(58,73)(59,71)(60,72)(61,74)(63,85)(64,92)(65,86)(67,69)(68,87)(70,80)(75,98)(76,95)(77,99)(78,102)(79,104)(81,89)(82,103)(83,105)(84,91)(88,111)(90,109)(93,115)(94,107)(96,100)(97,113)(101,110)(106,116)(108,117)(112,114);(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)(54,55,59,65,60,66,81,95,58,67,78,96,79,98,109,116,61,68,82,97,83,99,111,117,80,64,91,93,110,94,85,112)(56,69,71,100,72,75,89,106,73,87,102,113,104,77,90,108,74,92,103,115,105,107,88,114,70,62,84,86,101,57,63,76)

Polycyclic presentation:

2^8,53|a^2=e,c^2=e,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,d^a=dh,i^a=i^52,d^b=dh,i^b=i^52

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90133);