C₁₀₉×#3573 #28360827

order	13952
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₀₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₁₀₉×#3573

Subgroups

	subgroup	G/H
center	C₈×C₁₀₉	C₂⁴
commutator	C₂	C₂⁴×C₄×C₁₀₉
Frattini, cosocle	C₄	C₂⁵×C₁₀₉
socle	C₂×C₁₀₉	C₂⁴×C₄
prime radical	#585×C₁₀₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₀₉ ◁ G

1424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 3488

A minimal faithful permutation representation — 5 generators on 141 points:

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

Conjugacy classes & character table

7412 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₉×#12684, C₁₀₉×#12685, C₁₀₉×#21477, …
maximal normal subgroup of	C₁₀₉×#12684, C₁₀₉×#12685, C₁₀₉×#21477, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2305);

C109×#3573 #28360827