C₁₉×#2121 #14559978

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2121

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#99
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂³×C₁₉
prime radical	C₁₉×#534	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

280 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 84 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)(23,31,32,26)(24,27)(25,30,33,35)(29,34);(20,22)(21,25)(23,30)(24,29)(26,28)(27,33)(31,34)(32,35);(22,29)(25,33)(28,34)(30,35)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12705, C₁₉×#12706, C₁₉×#12725, …
maximal normal subgroup of	C₁₉×#12705, C₁₉×#12706, C₁₉×#12725, …
maximal quotient of	C₁₉×#11426, C₁₉×#11453, C₁₉×#11473, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 853);