C₂×C₁₉×#455 #14560872

order	2432
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₉×#455

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

760 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 608

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4,7,10)(5,11,13,18)(6,14,16,9)(8,15,17,12);(3,5)(4,8)(6,15)(7,13)(9,18)(10,17)(11,14)(12,16);(6,16)(9,14)(11,18)(12,15)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13048, C₁₉×#13050, C₁₉×#13348, …
maximal normal subgroup of	C₁₉×#13048, C₁₉×#13050, C₁₉×#13348, …
maximal quotient of	C₂×C₁₉×#1601, C₂×C₁₉×#1602, C₂×C₁₉×#1607, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1747);