C₂×C₄×C₁₆×C₁₀₁ #27167459

order	12928
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian

C₂×C₄×C₁₆×C₁₀₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
socle, prime radical	C₂³×C₁₀₁	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 3 generators on 123 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(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);(17,18,19,20);(21,22)

Conjugacy classes & character table

12928 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7136, C₁₀₁×#7141, C₁₀₁×#7154, …
maximal normal subgroup of	C₁₀₁×#7136, C₁₀₁×#7141, C₁₀₁×#7154, …
maximal quotient of	C₂×C₈×C₁₆×C₁₀₁, C₂×C₁₀₁×#1312, C₁₆×M₁₆×C₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 837);

C2×C4×C16×C101 #27167459