C₁₃×#3019 #13112077

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

Aliases

direct product

C₁₃×#3019

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

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

normal subgroups only

This group has 762 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)(14,15)(16,22)(17,25)(18,20)(19,23)(21,27)(24,29)(26,28);(14,16)(15,19)(17,26)(18,24)(20,28)(21,29)(22,25)(23,27);(17,27)(21,25)(22,29)(23,26);(15,20)(19,28)(21,25)(22,29)

Conjugacy classes & character table

377 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15894209, #15894220, #15894437, …
maximal subgroup of	C₁₃×#23872, C₁₃×#23873, C₁₃×#23892, …
maximal normal subgroup of	C₁₃×#23872, C₁₃×#23873, C₁₃×#23892, …
maximal quotient of	C₁₃×#18132, C₁₃×#18133, C₁₃×#18137, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1751);