C₁₀₃×#1508 #27190874

order	13184
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₃×#1508

Subgroups

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

294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 3 generators on 119 points:

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

Conjugacy classes & character table

3296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#8363, C₁₀₃×#8364, C₁₀₃×#8365, …
maximal normal subgroup of	C₁₀₃×#8363, C₁₀₃×#8364, C₁₀₃×#8365, …
maximal quotient of	C₁₀₃×#7573, C₁₀₃×#7575, C₁₀₃×#7583, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 240);