C₁₉×#2619 #14560476

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₉×#2619

Subgroups

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

728 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 1216

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)(24,25,26,27)(28,29)(30,33)(31,32)(34,35);(21,23)(29,32)(33,34);(20,21)(22,23)(24,25)(26,27)(28,29)(30,34)(31,32)(33,35);(28,30,31,35)(29,33,32,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9197, C₁₉×#9198, C₁₉×#11693, …
maximal normal subgroup of	C₁₉×#9197, C₁₉×#9198, C₁₉×#11693, …
maximal quotient of	C₁₉×#14257, C₁₉×#14260, C₁₉×#14272, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1351);