C₁₃×#2647 #13111705

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

Aliases

direct product

C₁₃×#2647

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

360 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 200 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)(15,16)(19,20)(22,23)(24,27)(25,28)(26,29)(30,31,34,32)(33,36,37,35);(14,15,18,16)(17,19,21,20)(22,24)(23,25)(26,28)(27,29)(30,32,34,31)(33,35,37,36);(14,16,18,15)(17,19,21,20)(22,24)(23,27)(25,29)(26,28)(30,33,34,37)(31,35,32,36);(14,17,18,21)(15,19,16,20)(22,25,26,27)(23,28,29,24)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15962681, #15962692, #15962705, …
maximal subgroup of	C₁₃×#29133, C₁₃×#29134, C₁₃×#29135, …
maximal normal subgroup of	C₁₃×#29133, C₁₃×#29134, C₁₃×#29135, …
maximal quotient of	C₁₃×#14266, C₁₃×#14276, C₁₃×#14277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1379);