C₁₀₁×#3095 #27168449

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₁×#3095

Subgroups

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

410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 3232

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

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

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#9346, C₁₀₁×#9362, C₁₀₁×#9363, …
maximal normal subgroup of	C₁₀₁×#9346, C₁₀₁×#9362, C₁₀₁×#9363, …
maximal quotient of	C₁₀₁×#20702, C₁₀₁×#20846, C₁₀₁×#20911, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1827);

C101×#3095 #27168449