C₁₉×#2503 #14560360

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#2503

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

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

normal subgroups only

This group has 512 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)(32,33,36,38)(34,35,37,39);(24,25,28,27)(26,29,30,31)(32,34)(33,35)(36,37)(38,39);(20,21,22,23)(24,26)(25,29)(27,31)(28,30)(32,35)(33,37)(34,38)(36,39);(24,27,28,25)(26,31,30,29)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9460, C₁₉×#9953, C₁₉×#9961, …
maximal normal subgroup of	C₁₉×#9460, C₁₉×#9953, C₁₉×#9961, …
maximal quotient of	C₁₉×#13881, C₁₉×#13904, C₁₉×#13972, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1235);