C₁₃×#1595 #13110653

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#1595

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

368 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 68 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)(15,19)(16,22)(20,26)(21,23)(24,28)(27,29);(14,15)(16,23)(17,21)(18,20)(19,22)(24,29)(25,27)(26,28);(16,24)(19,26)(22,28)(23,29)

Conjugacy classes & character table

299 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15774946, #15774956, #15774963, …
maximal subgroup of	C₁₃×#12090, C₁₃×#12092, C₁₃×#12093, …
maximal normal subgroup of	C₁₃×#12090, C₁₃×#12092, C₁₃×#12093, …
maximal quotient of	C₁₃×#7734, C₁₃×#7735, C₁₃×#7736, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 327);