C₁₃×#2785 #13111843

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₁₃×#2785

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

428 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 176 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)(14,15,18,16)(17,20,21,19)(22,23)(24,27)(25,26)(28,29)(31,32)(35,36);(15,16)(17,21)(23,25)(27,28)(30,31,34,32)(33,36,37,35);(14,16,18,15)(17,20,21,19)(22,24,26,29)(23,27,25,28)(30,32,34,31)(33,36,37,35);(14,17,18,21)(15,19,16,20)(22,25,26,23)(24,28,29,27)(30,33)(31,35)(32,36)(34,37)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15775278, #15775864, #16071875, …
maximal subgroup of	C₁₃×#12145, C₁₃×#12239, C₁₃×#36796, …
maximal normal subgroup of	C₁₃×#12145, C₁₃×#12239, C₁₃×#36796, …
maximal quotient of	C₁₃×#14399, C₁₃×#14476, C₁₃×#14589, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1517);