C₁₃×#2853 #13111911

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₃×#2853

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

582 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 832

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15896159, #15896783, #16035485, …
maximal subgroup of	C₁₃×#24057, C₁₃×#24113, C₁₃×#34983, …
maximal normal subgroup of	C₁₃×#24057, C₁₃×#24113, C₁₃×#34983, …
maximal quotient of	C₁₃×#14684, C₁₃×#14695, C₁₃×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1585);