C₁₉×#2211 #14560068

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×D₈×C₁₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 158 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)(21,23)(24,25)(26,34)(27,30)(28,40)(29,43)(31,36)(32,42)(33,39)(35,50)(37,54)(38,51)(41,49)(44,48)(45,52)(46,53)(47,55);(20,21,22,23)(25,30)(31,45)(32,46)(33,43)(34,50)(40,51)(47,49)(48,54);(24,26,27,35)(25,31,30,45)(28,41,38,55)(29,44,39,37)(32,48,46,54)(33,49,43,47)(34,51,50,40)(36,53,52,42)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2211, C₁₉×#33579, C₁₉×#33581, …
maximal normal subgroup of	C₂×C₁₉×#2211, C₁₉×#33579, C₁₉×#33581, …
maximal quotient of	C₁₉×#12419, C₁₉×#12423, C₁₉×#12429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 943);