C₁₃×#1437 #13110495

order	1664
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₃×#1437

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂³
commutator	C₂²	C₂×C₄²×C₁₃
Frattini, cosocle	C₂⁴	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

828 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

728 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15749944, #15754429, D₁₃×#1437, …
maximal subgroup of	C₁₃×#7213, C₁₃×#8346, C₂×C₁₃×#1437, …
maximal normal subgroup of	C₁₃×#7213, C₁₃×#8346, C₂×C₁₃×#1437, …
maximal quotient of	C₁₃×#7554, C₁₃×#7555, C₁₃×#7556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 169);