C₁₉×#1750 #14559607

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1750

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator	C₂²	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

336 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 168 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)(22,23)(24,25,27,26)(28,29)(30,33)(31,35)(32,34)(36,40)(37,39)(38,41)(42,43);(21,23)(28,30,31,36,32,37,38,42)(29,33,35,40,34,39,41,43);(24,26,27,25)(29,34)(33,39)(35,41)(40,43)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7214, C₁₉×#7216, C₁₉×#8348, …
maximal normal subgroup of	C₁₉×#7214, C₁₉×#7216, C₁₉×#8348, …
maximal quotient of	C₁₉×#8148, C₁₉×#8149, C₁₉×#8154, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 482);