C₁₉×#2823 #14560680

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2823

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

456 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 184 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)(24,25,27,29)(26,28,30,31)(32,33,36,37)(34,35,38,39);(21,23)(26,30)(28,31)(33,37)(35,39);(20,21)(22,23)(24,25)(26,28)(27,29)(30,31)(32,34)(33,35)(36,38)(37,39);(24,26,27,30)(25,28,29,31)(32,35)(33,38)(34,37)(36,39)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12155, C₁₉×#12249, C₂×C₁₉×#2823, …
maximal normal subgroup of	C₁₉×#12155, C₁₉×#12249, C₂×C₁₉×#2823, …
maximal quotient of	C₁₉×#14632, C₁₉×#14633, C₁₉×#14634, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1555);