C₁₉×#1819 #14559676

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1819

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

504 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7213, C₁₉×#7349, C₁₉×#8535, …
maximal normal subgroup of	C₁₉×#7213, C₁₉×#7349, C₁₉×#8535, …
maximal quotient of	C₁₉×#8698, C₁₉×#8700, C₁₉×#8702, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 551);