C₁₀₃×#13362 #39918637

order	26368
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₃×#13362

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₀₃
prime radical	#585×C₁₀₃	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₃ ◁ C₂×C₄×C₁₀₃ ◁ C₂×#41×C₁₀₃ ◁ G

670 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 167
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 3 generators on 167 points:

(1,2,8,13)(3,14,18,40)(4,19,24,44)(5,25,29,11)(6,30,7,12)(9,26,36,16)(10,23,39,22)(15,47,49,63)(17,52,31,46)(20,45,53,64)(21,56,27,54)(28,42,32,43)(33,57,62,55)(34,50,35,51)(37,48,61,60)(38,58,41,59)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167);(1,3)(2,9)(4,20)(5,26)(6,17)(7,31)(8,18)(10,37)(11,40)(12,34)(13,36)(14,25)(15,23)(16,29)(19,33)(21,57)(22,49)(24,53)(27,55)(28,51)(30,35)(32,50)(38,47)(39,61)(41,63)(42,52)(43,46)(44,62)(45,56)(48,58)(54,64)(59,60);(1,4,8,24)(2,10,13,39)(3,15,18,49)(5,27,29,21)(6,23,7,22)(9,33,36,62)(11,41,25,38)(12,44,30,19)(14,45,40,64)(16,48,26,60)(17,53,31,20)(28,58,32,59)(34,37,35,61)(42,54,43,56)(46,63,52,47)(50,57,51,55)

Conjugacy classes & character table

2884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 6350);