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C₁₃×#1336 #13110394

order	1664
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#102
commutator	C₈	C₂×C₈×C₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₃
socle	C₂×C₁₃	D₄⋊C₈
prime radical	C₁₃×#135	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#1336, #15772712, #15772998, …
maximal subgroup of	C₂×C₁₃×#1336, C₁₃×#11604, C₁₃×#11669, …
maximal normal subgroup of	C₂×C₁₃×#1336, C₁₃×#11604, C₁₃×#11669, …
maximal quotient of	C₁₃×#7070, C₁₃×#7071, C₁₃×#7072, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 68);