C₂×#494×C₁₀₃ #27192511

order	13184
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×#494×C₁₀₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 13184

A minimal faithful permutation representation — 4 generators on 125 points:

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

Conjugacy classes & character table

4532 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#9066, C₁₀₃×#9733, C₁₀₃×#9742, …
maximal normal subgroup of	C₁₀₃×#9066, C₁₀₃×#9733, C₁₀₃×#9742, …
maximal quotient of	C₂×C₁₀₃×#1707, C₂×C₁₀₃×#1710, C₂×C₁₀₃×#1713, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 1877);

C2×#494×C103 #27192511