C₁₉×#2388 #14560245

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#2388

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

944 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9009, C₁₉×#9010, C₁₉×#11725, …
maximal normal subgroup of	C₁₉×#9009, C₁₉×#9010, C₁₉×#11725, …
maximal quotient of	C₁₉×#13839, C₁₉×#13844, C₁₉×#13851, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1120);