C₁₃×#2371 #13111429

order	1664
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2371

Subgroups

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

448 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 280 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 — 4 generators on 33 points:

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

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15760543, #15760553, D₁₃×#2371, …
maximal subgroup of	C₁₃×#9440, C₁₃×#9442, C₂×C₁₃×#2371, …
maximal normal subgroup of	C₁₃×#9440, C₁₃×#9442, C₂×C₁₃×#2371, …
maximal quotient of	C₁₃×#13805, C₁₃×#13815, C₁₃×#13825, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1103);