C₂×#533×C₁₀₁ #27168797

order	12928
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₀₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×#533×C₁₀₁

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₀₁
socle	C₂³×C₁₀₁	C₂⁴
prime radical	C₂⁴×C₁₀₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 5 generators on 119 points:

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

Conjugacy classes & character table

5656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#8314, C₁₀₁×#8333, C₁₀₁×#8338, …
maximal normal subgroup of	C₁₀₁×#8314, C₁₀₁×#8333, C₁₀₁×#8338, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 2175);

C2×#533×C101 #27168797