C₁₉×#2817 #14560674

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

Aliases

direct product

C₁₉×#2817

Subgroups

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

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

normal subgroups only

This group has 444 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) = 47
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,28)(29,31)(32,33,37,35)(34,40,42,38)(36,39,45,43)(41,47,44,46);(21,23)(25,28)(26,30)(32,34,37,42)(33,38,35,40)(36,44,45,41)(39,47,43,46);(20,21)(22,23)(24,25)(26,29)(27,28)(30,31)(32,35,37,33)(34,38,42,40)(36,39,45,43)(41,47,44,46);(24,26)(25,29)(27,30)(28,31)(32,36,37,45)(33,39,35,43)(34,41,42,44)(38,46,40,47)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9982, C₁₉×#9985, C₁₉×#12095, …
maximal normal subgroup of	C₁₉×#9982, C₁₉×#9985, C₁₉×#12095, …
maximal quotient of	C₁₉×#14626, C₁₉×#14627, C₁₉×#14629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1549);