C₁₃×#2849 #13111907

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#2849

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

1102 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 1102 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) = 416

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

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15894506, #15894514, #15895371, …
maximal subgroup of	C₁₃×#23901, C₁₃×#23902, C₁₃×#23985, …
maximal normal subgroup of	C₁₃×#23901, C₁₃×#23902, C₁₃×#23985, …
maximal quotient of	C₁₃×#14681, C₁₃×#14693, C₁₃×#14694, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1581);