C₁₃×#2613 #13111671

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₃×#2613

Subgroups

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

1134 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 232 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)(19,21)(22,23)(24,27)(25,26)(28,29);(15,17)(19,21)(23,26)(27,28);(14,15)(16,17)(18,19)(20,21)(22,23)(24,28)(25,26)(27,29);(22,24)(23,27)(25,29)(26,28)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15836077, #15836099, #15894525, …
maximal subgroup of	C₁₃×#18224, C₁₃×#18226, C₁₃×#23903, …
maximal normal subgroup of	C₁₃×#18224, C₁₃×#18226, C₁₃×#23903, …
maximal quotient of	C₁₃×#14255, C₁₃×#14256, C₁₃×#14262, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1345);