C₁₃×#2551 #13111609

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#2551

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

556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 1664

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15765926, #15765931, #15765936, …
maximal subgroup of	C₁₃×#10348, C₁₃×#10349, C₁₃×#10350, …
maximal normal subgroup of	C₁₃×#10348, C₁₃×#10349, C₁₃×#10350, …
maximal quotient of	C₁₃×#13910, C₁₃×#14005, C₁₃×#14053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1283);