C₁₃×#2582 #13111640

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2582

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

484 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 33
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,22,20)(21,24,25,23)(26,27,30,33)(28,32,29,31);(19,20)(23,24)(26,28,30,29)(27,31,33,32);(14,15)(16,17)(18,20,22,19)(21,24,25,23)(26,27)(28,31)(29,32)(30,33);(18,21,22,25)(19,23,20,24)(26,29,30,28)(27,32,33,31)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15765228, #15765255, #15765273, …
maximal subgroup of	C₁₃×#10230, C₁₃×#10234, C₁₃×#10237, …
maximal normal subgroup of	C₁₃×#10230, C₁₃×#10234, C₁₃×#10237, …
maximal quotient of	C₁₃×#13926, C₁₃×#14017, C₁₃×#14041, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1314);