C₁₉×#3026 #14560883

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#3026

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

800 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 212 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)(22,25)(23,26)(24,27)(28,34)(29,32)(30,33)(31,35);(20,22)(21,25)(23,28)(24,29)(26,31)(27,32)(30,35)(33,34);(20,23)(21,26)(22,28)(24,30)(25,31)(27,33)(29,35)(32,34);(21,27)(25,32)(26,33)(31,34)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#23895, C₁₉×#23896, C₁₉×#23996, …
maximal normal subgroup of	C₁₉×#23895, C₁₉×#23896, C₁₉×#23996, …
maximal quotient of	C₁₉×#18284, C₁₉×#18285, C₁₉×#18286, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1758);