C₁₉×#2435 #14560292

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₉×#2435

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

1088 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9459, C₁₉×#9947, C₁₉×#9955, …
maximal normal subgroup of	C₁₉×#9459, C₁₉×#9947, C₁₉×#9955, …
maximal quotient of	C₁₉×#13881, C₁₉×#13902, C₁₉×#13971, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1167);