C₁₃×#1831 #13110889

order	1664
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#1831

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂³
commutator	C₂²	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

260 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 160 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) = 1664

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

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

Conjugacy classes & character table

728 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15749452, #15749461, #15749483, …
maximal subgroup of	C₁₃×#7018, C₁₃×#7022, C₁₃×#7030, …
maximal normal subgroup of	C₁₃×#7018, C₁₃×#7022, C₁₃×#7030, …
maximal quotient of	C₁₃×#8780, C₁₃×#8781, C₁₃×#8784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 563);