C₂×#472×C₁₀₉ #28360319

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

Aliases

direct product

C₂×#472×C₁₀₉

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₉	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂²×C₄×C₁₀₉ ◁ G

488 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)(5,12)(6,9)(11,16)(13,14)(15,17);(3,4,9,16,7,11,6,8)(5,10,12,17,14,18,13,15);(3,5)(4,10)(6,13)(7,14)(8,15)(9,12)(11,18)(16,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₉×#12996, C₁₀₉×#13007, C₁₀₉×#13068, …
maximal normal subgroup of	C₁₀₉×#12996, C₁₀₉×#13007, C₁₀₉×#13068, …
maximal quotient of	C₂×C₁₀₉×#1667, C₂×C₁₀₉×#1675, C₂×C₁₀₉×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 1797);

C2×#472×C109 #28360319