C₂×C₁₉×#359 #14559999

order	2432
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₁₉×#359

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	D₈
commutator	C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	#102
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

224 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 53
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53);(3,4,7,12,9,13,8,23)(5,14,16,30,17,31,24,28)(6,18,20,29,22,33,21,11)(10,19,25,32,27,34,26,15);(3,5)(4,10)(6,19)(7,16)(8,24)(9,17)(11,28)(12,25)(13,27)(14,18)(15,21)(20,32)(22,34)(23,26)(29,30)(31,33)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₁₉×#359, C₁₉×#12640, C₁₉×#12641, …
maximal normal subgroup of	C₄×C₁₉×#359, C₁₉×#12640, C₁₉×#12641, …
maximal quotient of	C₂×C₁₉×#1331, C₂×C₁₉×#1332, C₁₉×#11591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 874);