C₁₃×#2863 #13111921

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#2863

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

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

normal subgroups only

This group has 408 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)(14,15,19,18)(16,21,17,20)(22,23,26,29)(24,27,28,25)(32,36)(34,37);(14,16,19,17)(15,20,18,21)(22,24,26,28)(23,27,29,25)(30,31,33,35)(32,34,36,37);(14,17,19,16)(15,21,18,20)(22,25,26,27)(23,28,29,24);(14,18,19,15)(16,21,17,20)(22,23)(24,27)(25,28)(26,29)(30,32)(31,34)(33,36)(35,37)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15751318, #15751338, #15751410, …
maximal subgroup of	C₁₃×#7669, C₁₃×#7673, C₁₃×#7689, …
maximal normal subgroup of	C₁₃×#7669, C₁₃×#7673, C₁₃×#7689, …
maximal quotient of	C₁₃×#14688, C₁₃×#14699, C₁₃×#14703, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1595);