C₁₉×#2230 #14560087

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2230

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#476
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

126 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12364, C₁₉×#12365, C₁₉×#12366, …
maximal normal subgroup of	C₁₉×#12364, C₁₉×#12365, C₁₉×#12366, …
maximal quotient of	C₁₉×#12823, C₁₉×#12950, C₁₉×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 962);