C₂×C₁₃×#487 #13112187

order	1664
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₁₃×#487

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 424 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) = 31
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4)(5,8)(6,7)(9,10)(11,12,16,17)(13,18,14,15);(4,7)(8,10)(11,13,15,12,16,14,18,17);(3,5,6,9)(4,8,7,10)(11,14,15,17,16,13,18,12)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15758191, #15758220, #15762179, …
maximal subgroup of	C₁₃×#9060, C₁₃×#9065, C₁₃×#9736, …
maximal normal subgroup of	C₁₃×#9060, C₁₃×#9065, C₁₃×#9736, …
maximal quotient of	C₂×C₁₃×#1834, C₂×C₁₃×#1933, C₂×C₁₃×#1956, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1861);