C₂×#471×C₁₀₉ #28360318

order	13952
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#471×C₁₀₉

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₉	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₉
prime radical	C₂×AGL(1,ℤ/8)×C₁₀₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂²×C₄×C₁₀₉ ◁ G

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 127
transitive degree	μ_t(G) = 3488

A minimal faithful permutation representation — 4 generators on 127 points:

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

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×#471×C₁₀₉, C₁₀₉×#21557, C₁₀₉×#23044, …
maximal normal subgroup of	C₄×#471×C₁₀₉, C₁₀₉×#21557, C₁₀₉×#23044, …
maximal quotient of	C₂×C₁₀₉×#1665, C₂×C₁₀₉×#1671, C₂×C₁₀₉×#1681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 1796);

C2×#471×C109 #28360318