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#27304706

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

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

Polycyclic presentation:

2^8,53|a^2=e,c^2=e,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ch,d^a=df,f^a=fg,g^a=gh,i^a=i^52,d^b=df,f^b=fg,g^b=gh,i^b=i^52

Conjugacy classes & character table

2132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90182);