C₁₃×#3021 #13112079

order	1664
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#3021

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

736 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 generators on 29 points:

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

Conjugacy classes & character table

377 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15781918, #15781925, #15781963, …
maximal subgroup of	C₁₃×#13353, C₁₃×#13354, C₁₃×#13360, …
maximal normal subgroup of	C₁₃×#13353, C₁₃×#13354, C₁₃×#13360, …
maximal quotient of	C₁₃×#18135, C₁₃×#18141, C₁₃×#18145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1753);