C₁₀₃×#3022 #27192388

order	13184
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₀₃×#3022

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₃	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₃
prime radical	#585×C₁₀₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₃ ◁ C₂²×C₄×C₁₀₃ ◁ G

704 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 212 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) = 135
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 4 generators on 135 points:

(1,2,6,10)(3,11,15,22)(4,8,18,26)(5,19,20,9)(7,13,23,14)(12,28,30,27)(16,25,17,24)(21,31,32,29)(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)(2,7)(4,12)(5,13)(6,15)(8,21)(9,22)(10,23)(11,19)(14,20)(16,29)(17,31)(18,30)(24,28)(25,27)(26,32);(1,4)(2,8)(3,12)(5,16)(6,18)(7,21)(9,24)(10,26)(11,27)(13,29)(14,31)(15,30)(17,20)(19,25)(22,28)(23,32);(1,5,6,20)(2,9,10,19)(3,13,15,14)(4,16,18,17)(7,22,23,11)(8,24,26,25)(12,29,30,31)(21,28,32,27)

Conjugacy classes & character table

2987 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#13355, C₁₀₃×#13356, C₁₀₃×#13361, …
maximal normal subgroup of	C₁₀₃×#13355, C₁₀₃×#13356, C₁₀₃×#13361, …
maximal quotient of	C₁₀₃×#18136, C₁₀₃×#18140, C₁₀₃×#18146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 1754);