C₁₉×#2733 #14560590

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₉×#2733

Subgroups

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

592 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 192 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 — 4 generators on 39 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7742, C₁₉×#7758, C₁₉×#7781, …
maximal normal subgroup of	C₁₉×#7742, C₁₉×#7758, C₁₉×#7781, …
maximal quotient of	C₁₉×#14399, C₁₉×#14445, C₁₉×#14467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1465);