C₂×#575×C₁₀₉ #28360834

order	13952
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₀₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×#575×C₁₀₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₀₉	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₁₀₉
socle	C₂²×C₁₀₉	C₂²×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₉ ◁ C₂³×C₄×C₁₀₉ ◁ G

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 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);(3,4)(5,12)(6,11)(7,15)(8,10)(9,13)(14,18)(16,17);(3,5)(4,9)(6,13)(7,16)(8,14)(10,17)(11,18)(12,15);(4,10)(9,17)(11,15)(12,18);(3,6,8,7)(4,11,10,15)(5,13,14,16)(9,18,17,12)

Conjugacy classes & character table

4796 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₉×#11018, C₁₀₉×#11019, C₁₀₉×#11032, …
maximal normal subgroup of	C₁₀₉×#11018, C₁₀₉×#11019, C₁₀₉×#11032, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2312);

C2×#575×C109 #28360834