C₁₉×#2219 #14560076

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2219

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

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

normal subgroups only

This group has 150 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) = 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)(26,34,36,48)(27,39,41,54)(28,42,40,32)(30,43,44,37)(31,46,47,35)(38,53,52,50)(45,51,49,55);(24,26,35,51,28,38,41,43,29,36,46,55,40,52,27,37)(25,30,39,50,32,45,47,48,33,44,54,53,42,49,31,34);(21,23)(26,36)(30,44)(34,48)(37,43)(38,52)(45,49)(50,53)(51,55)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7423, C₁₉×#7425, C₁₉×#13668, …
maximal normal subgroup of	C₁₉×#7423, C₁₉×#7425, C₁₉×#13668, …
maximal quotient of	C₁₉×#12434, C₁₉×#12443, C₁₉×#12455, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 951);