C₁₃×#2641 #13111699

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₃×#2641

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

584 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 33
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,23)(21,22)(24,25)(27,30)(31,32);(14,15,16,17)(19,22)(23,24)(26,27,29,30)(28,31,33,32);(14,15)(16,17)(18,19)(20,24)(21,22)(23,25)(26,27)(28,32)(29,30)(31,33);(18,20,21,25)(19,23,22,24)(26,28,29,33)(27,31,30,32)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15764268, #15764324, #15838031, …
maximal subgroup of	C₁₃×#10089, C₁₃×#10097, C₁₃×#18430, …
maximal normal subgroup of	C₁₃×#10089, C₁₃×#10097, C₁₃×#18430, …
maximal quotient of	C₁₃×#14260, C₁₃×#14272, C₁₃×#14283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1373);