C₁₃×#2859 #13111917

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2859

Subgroups

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

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

normal subgroups only

This group has 472 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)(15,17)(20,23)(21,25)(26,27,31,30)(28,33,32,29);(18,19,22,24)(20,21,23,25)(26,28)(27,29)(30,33)(31,32);(14,15,16,17)(18,20,22,23)(19,21,24,25)(26,29,31,33)(27,32,30,28);(18,21)(19,23)(20,24)(22,25)(26,30,31,27)(28,33,32,29)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15751279, #15751292, #15751371, …
maximal subgroup of	C₁₃×#7660, C₁₃×#7663, C₁₃×#7680, …
maximal normal subgroup of	C₁₃×#7660, C₁₃×#7663, C₁₃×#7680, …
maximal quotient of	C₁₃×#14687, C₁₃×#14699, C₁₃×#14707, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1591);