C₁₀₁×#3531 #27168885

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

Aliases

direct product

C₁₀₁×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₀₁
socle	C₂²×C₁₀₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ G

930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 5 generators on 133 points:

(1,2)(3,6)(4,11)(5,8)(7,13)(9,16)(10,15)(12,14)(17,18)(19,25)(20,24)(21,23)(22,26)(27,31)(28,30)(29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133);(1,3,5,10)(2,6,8,15)(4,12,13,9)(7,16,11,14)(17,19)(18,22)(20,27)(21,26)(23,25)(24,29)(28,32)(30,31);(1,4,5,13)(2,7,8,11)(3,9,10,12)(6,14,15,16)(19,26)(22,25)(27,32)(29,31);(2,8)(6,15)(7,11)(14,16)(18,23)(19,26)(24,30)(27,32);(17,20,21,28)(18,24,23,30)(19,27,26,32)(22,29,25,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#8505, C₁₀₁×#18990, C₁₀₁×#18991, …
maximal normal subgroup of	C₁₀₁×#8505, C₁₀₁×#18990, C₁₀₁×#18991, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 2263);