C₁₃×#2382 #13111440

order	1664
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2382

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

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

normal subgroups only

This group has 408 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) = 1664

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

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15757287, #15757293, #15757303, …
maximal subgroup of	C₁₃×#8912, C₁₃×#8913, C₁₃×#8915, …
maximal normal subgroup of	C₁₃×#8912, C₁₃×#8913, C₁₃×#8915, …
maximal quotient of	C₁₃×#13829, C₁₃×#13833, C₁₃×#14385, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1114);