C₁₉×#1699 #14559556

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1699

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1699, C₁₉×#19142, C₁₉×#19156, …
maximal normal subgroup of	C₂×C₁₉×#1699, C₁₉×#19142, C₁₉×#19156, …
maximal quotient of	C₁₉×#8654, C₁₉×#9225, C₁₉×#9227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 431);