C₁₉×#2401 #14560258

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2401

Subgroups

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

432 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,31,33)(30,32,34,35)(36,37,39,41)(38,40,42,43);(21,24)(25,27)(28,30,31,34)(29,32,33,35)(36,38)(37,40)(39,42)(41,43);(29,33)(32,35)(38,42)(40,43);(20,22,23,26)(21,25,24,27)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#21668, C₁₉×#21669, C₁₉×#21670, …
maximal normal subgroup of	C₁₉×#21668, C₁₉×#21669, C₁₉×#21670, …
maximal quotient of	C₁₉×#13842, C₁₉×#13846, C₁₉×#13855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1133);