C₁₁₃×#1909 #28386705

order	14464
nilpotency class	3
isoclinism	isoclinic class of #1909
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁₃×#1909

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁₃	#386
commutator	C₂×C₄	C₂²×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₁₃
prime radical	C₂×#41×C₁₁₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁₃ ◁ C₂²×C₄×C₁₁₃ ◁ G

312 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 145
transitive degree	μ_t(G) = 3616

A minimal faithful permutation representation — 3 generators on 145 points:

(1,2)(3,11)(4,15,17,8)(5,18)(6,10)(7,13)(9,20)(12,25,28,32)(14,26)(16,23,19,24)(21,27,31,29)(22,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(1,3,5,13,6,14,20,30)(2,7,9,11,10,22,18,26)(4,12,19,29,17,28,16,27)(8,21,24,25,15,31,23,32);(1,4)(2,8)(3,12)(5,19)(6,17)(7,21)(9,24)(10,15)(11,25)(13,29)(14,28)(16,20)(18,23)(22,31)(26,32)(27,30)

Conjugacy classes & character table

3277 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#12756, C₁₁₃×#12757, C₁₁₃×#12779, …
maximal normal subgroup of	C₁₁₃×#12756, C₁₁₃×#12757, C₁₁₃×#12779, …
maximal quotient of	C₁₁₃×#9099, C₁₁₃×#9100, C₁₁₃×#9103, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 641);