C₁₉×#1785 #14559642

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#1785

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

584 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 608

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)(20,21)(22,23)(24,25,28,33,29,32,27,31)(26,34,35,39,36,30,37,38);(24,26)(25,30)(27,35)(28,37)(29,36)(31,38)(32,34)(33,39);(21,23)(24,27,29,28)(25,31,32,33)(26,35,36,37)(30,38,34,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7306, C₁₉×#7309, C₁₉×#7312, …
maximal normal subgroup of	C₁₉×#7306, C₁₉×#7309, C₁₉×#7312, …
maximal quotient of	C₁₉×#8300, C₁₉×#8301, C₁₉×#8304, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 517);