C₁₃×#3291 #13112349

order	1664
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#3291

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ G

460 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 184 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)(14,15,20,25)(16,26,27,28)(17,22,21,29)(18,24,19,23);(14,16)(15,21)(17,25)(18,29)(19,22)(20,27)(23,28)(24,26);(14,17)(15,16)(18,28)(19,26)(20,21)(22,23)(24,29)(25,27);(14,17)(15,22)(16,23)(18,26)(19,28)(20,21)(24,27)(25,29)

Conjugacy classes & character table

377 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15776332, #15776337, #15776678, …
maximal subgroup of	C₁₃×#12314, C₁₃×#12315, C₁₃×#12364, …
maximal normal subgroup of	C₁₃×#12314, C₁₃×#12315, C₁₃×#12364, …
maximal quotient of	C₁₃×#19884, C₁₃×#19888, C₁₃×#19890, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2023);