C₁₃×#1600 #13110658

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#1600

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

320 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

299 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#1600, #15835124, #15835222, …
maximal subgroup of	C₂×C₁₃×#1600, C₁₃×#18114, C₁₃×#18126, …
maximal normal subgroup of	C₂×C₁₃×#1600, C₁₃×#18114, C₁₃×#18126, …
maximal quotient of	C₁₃×#7737, C₁₃×#7740, C₁₃×#7742, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 332);