C₁₃×#2571 #13111629

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

Aliases

direct product

C₁₃×#2571

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

380 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15765943, #15765948, #15765953, …
maximal subgroup of	C₁₃×#10351, C₁₃×#10352, C₁₃×#10353, …
maximal normal subgroup of	C₁₃×#10351, C₁₃×#10352, C₁₃×#10353, …
maximal quotient of	C₁₃×#13911, C₁₃×#13982, C₁₃×#14030, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1303);