C₁₉×#2853 #14560710

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#2853

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

582 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 216 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)(21,23)(25,27)(26,30)(33,36)(34,38);(24,25,28,27)(26,29,30,31)(32,33)(34,37)(35,36)(38,39);(24,26)(25,29)(27,31)(28,30);(20,21)(22,23)(24,27,28,25)(26,31,30,29)(32,34,35,38)(33,37,36,39)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#24057, C₁₉×#24113, C₁₉×#34983, …
maximal normal subgroup of	C₁₉×#24057, C₁₉×#24113, C₁₉×#34983, …
maximal quotient of	C₁₉×#14684, C₁₉×#14695, C₁₉×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1585);