C₂×C₄×D₈×C₁₀₃ #27192302

order	13184
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₄×D₈×C₁₀₃

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₃	D₄
commutator	C₄	C₂³×C₄×C₁₀₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₃
socle	C₂³×C₁₀₃	C₂×D₄
prime radical	C₂²×D₈×C₁₀₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 4 generators on 117 points:

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

Conjugacy classes & character table

5768 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#8947, C₁₀₃×#8951, C₁₀₃×#9657, …
maximal normal subgroup of	C₁₀₃×#8947, C₁₀₃×#8951, C₁₀₃×#9657, …
maximal quotient of	C₂×C₈×D₈×C₁₀₃, C₂×C₁₀₃×#1581, C₂×C₁₀₃×#1589, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 1668);

C2×C4×D8×C103 #27192302