C₁₉×#1720 #14559577

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#1720

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₁₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

186 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 72 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)(20,21,25,22)(23,24,27,26)(28,29,32,35)(30,36,38,43)(31,40,37,34)(33,41,42,39);(20,22,24,27,25,21,26,23)(28,30,37,41,32,38,31,39)(29,33,40,43,35,42,34,36);(20,23,24,22,25,27,26,21)(30,38)(33,42)(36,43)(39,41)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1720, C₁₉×#19613, C₁₉×#19619, …
maximal normal subgroup of	C₂×C₁₉×#1720, C₁₉×#19613, C₁₉×#19619, …
maximal quotient of	C₁₉×#8821, C₁₉×#9827, C₁₉×#9828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 452);