C₁₃×#3184 #13112242

order	1664
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₃×#3184

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 446 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) = 832

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15760410, #15773766, #15839241, …
maximal subgroup of	C₁₃×#9417, C₁₃×#11837, C₁₃×#18554, …
maximal normal subgroup of	C₁₃×#9417, C₁₃×#11837, C₁₃×#18554, …
maximal quotient of	C₁₃×#20824, C₁₃×#21286, C₁₃×#21410, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1916);