C₁₉×#1695 #14559552

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#1695

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 68 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 68 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)(20,21,23,26)(22,24,27,25)(28,29,32,35)(30,36,38,43)(31,40,37,34)(33,41,42,39);(28,30,37,41,32,38,31,39)(29,33,40,43,35,42,34,36);(21,24)(22,27)(25,26)(30,38)(33,42)(36,43)(39,41)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12376, C₁₉×#12377, C₁₉×#12400, …
maximal normal subgroup of	C₁₉×#12376, C₁₉×#12377, C₁₉×#12400, …
maximal quotient of	C₁₉×#8652, C₁₉×#9223, C₁₉×#9575, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 427);