C₁₀₃×#1407 #27190773

order	13184
nilpotency class	5
isoclinism	isoclinic class of #1406
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₀₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₃×#1407

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₃	#353
commutator	C₄²	C₂×C₄×C₁₀₃
Frattini, cosocle	#124	C₂²×C₁₀₃
prime radical	C₂×D₄×C₁₀₃	D₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₃ ◁ C₂²×C₁₀₃ ◁ C₂×C₄×C₁₀₃ ◁ #124×C₁₀₃ ◁ G

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 135
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 2 generators on 135 points:

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

Conjugacy classes & character table

1442 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₃×#1407, C₁₀₃×#13577, C₁₀₃×#13578, …
maximal normal subgroup of	C₂×C₁₀₃×#1407, C₁₀₃×#13577, C₁₀₃×#13578, …
maximal quotient of	C₁₀₃×#7353, C₁₀₃×#7372, C₁₀₃×#7403, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 139);

C103×#1407 #27190773