C₄×#95×C₁₀₉ #28358686

order	13952
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄³×C₁₀₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₄×#95×C₁₀₉

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₁₀₉	C₂²
commutator	C₂	C₄³×C₁₀₉
Frattini, cosocle	C₂⁴	C₂³×C₁₀₉
socle, prime radical	C₂⁴×C₁₀₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₉ ◁ G

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 13952

A minimal faithful permutation representation — 3 generators on 125 points:

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

Conjugacy classes & character table

8720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₉×#7017, C₁₀₉×#7028, C₄×#327×C₁₀₉, …
maximal normal subgroup of	C₁₀₉×#7017, C₁₀₉×#7028, C₄×#327×C₁₀₉, …
maximal quotient of	C₁₀₉×#7554, C₄×#336×C₁₀₉, C₁₀₉×#10693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 164);

C4×#95×C109 #28358686