C₁₃×#2858 #13111916

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₃×#2858

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

752 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15751275, #15751367, #15751459, …
maximal subgroup of	C₁₃×#7659, C₁₃×#7679, C₁₃×#7699, …
maximal normal subgroup of	C₁₃×#7659, C₁₃×#7679, C₁₃×#7699, …
maximal quotient of	C₁₃×#14687, C₁₃×#14700, C₁₃×#14708, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1590);