C₁₃×#3058 #13112116

order	1664
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₃×#3058

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

524 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 416

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15773913, #15773921, #15780369, …
maximal subgroup of	C₁₃×#11868, C₁₃×#11870, C₁₃×#13074, …
maximal normal subgroup of	C₁₃×#11868, C₁₃×#11870, C₁₃×#13074, …
maximal quotient of	C₁₃×#19187, C₁₃×#19192, C₁₃×#19198, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1790);