C₁₃×#2643 #13111701

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#2643

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

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

normal subgroups only

This group has 462 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) = 37
transitive degree	μ_t(G) = 832

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

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

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#2643, #16029449, #16029610, …
maximal subgroup of	C₂×C₁₃×#2643, C₁₃×#34570, C₁₃×#34584, …
maximal normal subgroup of	C₂×C₁₃×#2643, C₁₃×#34570, C₁₃×#34584, …
maximal quotient of	C₁₃×#14259, C₁₃×#14265, C₁₃×#14331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1375);