C₁₉×#2210 #14560067

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

Aliases

direct product

C₁₉×#2210

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 170 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25)(26,29)(27,30)(28,36)(31,35)(32,34)(33,37)(38,39);(20,21,22,23)(25,29)(30,37)(31,38)(32,36);(25,30)(27,35)(28,34)(29,37)(31,32)(33,39)(36,38)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2210, C₁₉×#33579, C₁₉×#33580, …
maximal normal subgroup of	C₂×C₁₉×#2210, C₁₉×#33579, C₁₉×#33580, …
maximal quotient of	C₁₉×#12418, C₁₉×#12422, C₁₉×#12428, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 942);