C₁₀₉×#2148 #28359402

order	13952
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₉×#2148

Subgroups

	subgroup	G/H
center	C₄×C₁₀₉	#102
commutator	C₈	C₂²×C₄×C₁₀₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₀₉
socle	C₂×C₁₀₉	C₂×#102
prime radical	C₂×#135×C₁₀₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₉ ◁ C₂²×C₄×C₁₀₉ ◁ C₂²×C₈×C₁₀₉ ◁ G

220 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 141
transitive degree	μ_t(G) = 3488

A minimal faithful permutation representation — 3 generators on 141 points:

(1,2,4,8,6,11,18,10)(3,12,15,26,16,29,13,28)(5,19,17,9,21,25,30,27)(7,20,23,14,24,31,22,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3)(2,7)(4,13)(5,20)(6,16)(8,22)(9,26)(10,23)(11,24)(12,25)(14,30)(15,18)(17,32)(19,29)(21,31)(27,28);(1,4,6,18)(2,8,11,10)(3,13,16,15)(5,17,21,30)(7,22,24,23)(9,25,27,19)(12,28,29,26)(14,20,32,31)

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₉×#12646, C₁₀₉×#12651, C₁₀₉×#12740, …
maximal normal subgroup of	C₁₀₉×#12646, C₁₀₉×#12651, C₁₀₉×#12740, …
maximal quotient of	C₁₀₉×#11597, C₁₀₉×#11598, C₁₀₉×#11651, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 880);