C₆₇×#32949 #30712200

order	17152
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₆₇×#32949

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	#585×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

1278 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 131
transitive degree	μ_t(G) = 4288

A minimal faithful permutation representation — 4 generators on 131 points:

(1,2,7,12)(3,13,18,36)(4,9,21,31)(5,10,23,33)(6,24,14,11)(8,25,28,17)(15,34,41,56)(16,35,43,57)(19,44,46,29)(20,47,37,30)(22,48,38,32)(26,49,52,40)(27,50,53,42)(39,59,61,55)(45,54,58,63)(51,60,62,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(1,3,14,25,7,18,6,17)(2,8,24,36,12,28,11,13)(4,15,37,49,21,41,20,40)(5,16,38,50,23,43,22,42)(9,26,47,56,31,52,30,34)(10,27,48,57,33,53,32,35)(19,39,58,64,46,61,45,60)(29,51,63,59,44,62,54,55);(1,4)(2,9)(3,15)(5,19)(6,20)(7,21)(8,26)(10,29)(11,30)(12,31)(13,34)(14,37)(16,39)(17,40)(18,41)(22,45)(23,46)(24,47)(25,49)(27,51)(28,52)(32,54)(33,44)(35,55)(36,56)(38,58)(42,60)(43,61)(48,63)(50,64)(53,62)(57,59);(1,5)(2,10)(3,16)(4,19)(6,22)(7,23)(8,27)(9,29)(11,32)(12,33)(13,35)(14,38)(15,39)(17,42)(18,43)(20,45)(21,46)(24,48)(25,50)(26,51)(28,53)(30,54)(31,44)(34,55)(36,57)(37,58)(40,60)(41,61)(47,63)(49,64)(52,62)(56,59)

Conjugacy classes & character table

3082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 25937);