C₁₃×#3292 #13112350

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

Aliases

direct product

C₁₃×#3292

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

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

normal subgroups only

This group has 476 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)(16,27)(17,23)(18,25)(19,24)(20,26)(21,28)(22,29);(14,16,20,22)(15,21,26,17)(18,23,19,28)(24,29,25,27);(14,17)(15,22)(16,26)(18,29)(19,27)(20,21)(23,24)(25,28);(14,17)(15,23)(16,25)(18,27)(19,29)(20,21)(22,24)(26,28)

Conjugacy classes & character table

377 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15776312, #15776322, #15776688, …
maximal subgroup of	C₁₃×#12310, C₁₃×#12312, C₁₃×#12366, …
maximal normal subgroup of	C₁₃×#12310, C₁₃×#12312, C₁₃×#12366, …
maximal quotient of	C₁₃×#19885, C₁₃×#19893, C₁₃×#19898, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2024);