C₁₃×#1967 #13111025

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#1967

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

312 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 416

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15755216, #15755223, #15766877, …
maximal subgroup of	C₁₃×#8483, C₁₃×#8484, C₁₃×#10496, …
maximal normal subgroup of	C₁₃×#8483, C₁₃×#8484, C₁₃×#10496, …
maximal quotient of	C₁₃×#9651, C₁₃×#9652, C₁₃×#9687, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 699);