C₁₉×#2883 #14560740

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#2883

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

800 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 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)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33);(20,22)(21,25)(23,29)(24,30)(26,32)(27,28)(31,35)(33,34);(20,23)(21,26)(22,29)(24,31)(25,32)(27,33)(28,34)(30,35);(23,31)(26,33)(29,35)(32,34)

Conjugacy classes & character table

779 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13100, C₁₉×#13102, C₁₉×#21776, …
maximal normal subgroup of	C₁₉×#13100, C₁₉×#13102, C₁₉×#21776, …
maximal quotient of	C₁₉×#17350, C₁₉×#17351, C₁₉×#17367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1615);