C₁₃×#2113 #13111171

order	1664
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#2113

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂³
commutator	C₂²	C₂²×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂²×C₈
prime radical	C₂×C₁₃×#41	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

228 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,25,22,26,31,37,23,27,32,38,33,39,43,47)(20,24,29,35,30,36,42,46,28,34,40,44,41,45,48,49);(15,17)(18,20)(19,24)(21,29)(22,30)(23,28)(25,35)(26,36)(27,34)(31,42)(32,40)(33,41)(37,46)(38,44)(39,45)(43,48)(47,49);(20,28)(24,34)(29,40)(30,41)(35,44)(36,45)(42,48)(46,49)

Conjugacy classes & character table

728 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15749926, #15749929, #15749986, …
maximal subgroup of	C₁₃×#7207, C₁₃×#7208, C₁₃×#7227, …
maximal normal subgroup of	C₁₃×#7207, C₁₃×#7208, C₁₃×#7227, …
maximal quotient of	C₁₃×#11419, C₁₃×#11441, C₁₃×#11461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 845);