C₁₀₁×#3381 #27168735

order	12928
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₁×#3381

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
prime radical	C₂×D₄×C₁₀₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄×Q₈×C₁₀₁ ◁ G

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 4 generators on 125 points:

(1,2,5,4)(3,7,8,6)(9,10,13,17)(11,14,19,23)(12,15,20,16)(18,21,24,22)(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);(1,3,5,8)(2,6,4,7)(9,11,13,19)(10,14,17,23)(12,18,20,24)(15,21,16,22);(10,15)(12,20)(14,21)(16,17)(18,24)(22,23);(1,4,5,2)(3,6,8,7)

Conjugacy classes & character table

3535 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#19790, C₁₀₁×#19797, C₁₀₁×#19807, …
maximal normal subgroup of	C₁₀₁×#19790, C₁₀₁×#19797, C₁₀₁×#19807, …
maximal quotient of	C₁₀₁×#22519, C₁₀₁×#22521, C₄⋊C₄×SD₁₆×C₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 2113);

C101×#3381 #27168735