C₁₉×#1703 #14559560

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

Aliases

direct product

C₁₉×#1703

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

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

normal subgroups only

This group has 154 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1703, C₁₉×#19142, C₁₉×#19158, …
maximal normal subgroup of	C₂×C₁₉×#1703, C₁₉×#19142, C₁₉×#19158, …
maximal quotient of	C₁₉×#8656, C₁₉×#9223, C₁₉×#9227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 435);