C₁₉×#2216 #14560073

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2216

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,29,33)(26,34,38,50)(27,39,41,54)(28,42,40,32)(30,43,45,36)(31,46,47,35)(37,53,52,49)(44,51,48,55);(24,26,35,51,28,37,41,43,29,38,46,55,40,52,27,36)(25,30,39,49,32,44,47,50,33,45,54,53,42,48,31,34);(21,23)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7419, C₁₉×#7421, C₁₉×#13664, …
maximal normal subgroup of	C₁₉×#7419, C₁₉×#7421, C₁₉×#13664, …
maximal quotient of	C₁₉×#12431, C₁₉×#12440, C₁₉×#12452, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 948);