D₄×M₁₆×C₁₀₃ #27192300

order	13184
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

D₄×M₁₆×C₁₀₃

Subgroups

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

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 115
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 4 generators on 115 points:

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

Conjugacy classes & character table

5150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#8906, C₁₀₃×#8908, C₁₀₃×#8989, …
maximal normal subgroup of	C₁₀₃×#8906, C₁₀₃×#8908, C₁₀₃×#8989, …
maximal quotient of	M₁₆×D₈×C₁₀₃, C₁₀₃×#18035, M₁₆×SD₁₆×C₁₀₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 1666);

D4×M16×C103 #27192300