C₁₀₁×#2246 #27167600

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₀₁×#2246

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 3 generators on 121 points:

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

Conjugacy classes & character table

3838 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7444, C₁₀₁×#7448, C₁₀₁×#12316, …
maximal normal subgroup of	C₁₀₁×#7444, C₁₀₁×#7448, C₁₀₁×#12316, …
maximal quotient of	C₁₀₁×#12503, C₁₀₁×#12509, C₁₀₁×#12515, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 978);

C101×#2246 #27167600