C₁₃×#3531 #13112589

order	1664
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₁₃×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 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) = 45
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 5 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,21)(18,20)(19,23)(24,28)(25,27)(26,29)(30,31)(32,35)(33,40)(34,37)(36,42)(38,45)(39,44)(41,43);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32,34,39)(31,35,37,44)(33,41,42,38)(36,45,40,43);(16,23)(19,22)(24,29)(26,28)(30,33,34,42)(31,36,37,40)(32,38,39,41)(35,43,44,45);(15,20)(16,23)(21,27)(24,29)(31,37)(35,44)(36,40)(43,45);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15755357, #15844117, #15844129, …
maximal subgroup of	C₁₃×#8505, C₁₃×#18990, C₁₃×#18991, …
maximal normal subgroup of	C₁₃×#8505, C₁₃×#18990, C₁₃×#18991, …
maximal quotient of	C₁₃×#34348, C₁₃×#34350, C₄×C₁₃×#562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2263);