C₁₃×#2629 #13111687

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2629

Subgroups

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

472 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 832

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15904273, #15904303, #15904333, …
maximal subgroup of	C₁₃×#24713, C₁₃×#24715, C₁₃×#24717, …
maximal normal subgroup of	C₁₃×#24713, C₁₃×#24715, C₁₃×#24717, …
maximal quotient of	C₁₃×#14264, C₁₃×#14266, C₁₃×#14276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1361);