C₁₃×#1935 #13110993

order	1664
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#1935

Subgroups

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

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

normal subgroups only

This group has 248 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) = 29
transitive degree	μ_t(G) = 1664

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

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#1935, #15865553, #15865564, …
maximal subgroup of	C₂×C₁₃×#1935, C₁₃×#21086, C₁₃×#21087, …
maximal normal subgroup of	C₂×C₁₃×#1935, C₁₃×#21086, C₁₃×#21087, …
maximal quotient of	C₁₃×#9555, C₁₃×#9559, C₁₃×#9569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 667);