C₁₀₃×#2241 #27191607

order	13184
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₃×#2241

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₀₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₄²×C₁₀₃ ◁ C₄×C₈×C₁₀₃ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 127
transitive degree	μ_t(G) = 13184

A minimal faithful permutation representation — 3 generators on 127 points:

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

Conjugacy classes & character table

3914 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#12344, C₁₀₃×#12345, C₁₀₃×#12346, …
maximal normal subgroup of	C₁₀₃×#12344, C₁₀₃×#12345, C₁₀₃×#12346, …
maximal quotient of	C₁₀₃×#12888, C₁₀₃×#13148, C₁₀₃×#13203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 973);

C103×#2241 #27191607