C₁₃×#2379 #13111437

order	1664
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₃×#2379

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

520 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 264 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)(14,15,16,17)(19,22)(20,24)(26,27)(28,32)(29,30)(31,33);(19,22)(23,25)(27,30)(28,33);(18,19,21,22)(20,23,24,25)(26,27)(28,31)(29,30)(32,33);(18,20)(19,23)(21,24)(22,25)(26,28,29,33)(27,31,30,32)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15757274, #15757280, #15757298, …
maximal subgroup of	C₁₃×#8910, C₁₃×#8911, C₁₃×#8914, …
maximal normal subgroup of	C₁₃×#8910, C₁₃×#8911, C₁₃×#8914, …
maximal quotient of	C₁₃×#13829, C₁₃×#13831, C₁₃×#13832, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1111);