C₁₉×#1512 #14559369

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

222 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,23)(26,27)(28,29)(30,36,38,33)(31,34)(32,35)(37,42,43,40)(39,41);(20,21)(22,25)(23,27)(24,26)(28,30)(29,33)(31,37)(32,38)(34,40)(35,36)(39,43)(41,42);(20,22,24,23)(21,25,26,27)(28,31,32,39)(29,34,35,41)(30,37,38,43)(33,40,36,42)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8497, C₁₉×#8498, C₁₉×#8499, …
maximal normal subgroup of	C₁₉×#8497, C₁₉×#8498, C₁₉×#8499, …
maximal quotient of	C₁₉×#7594, C₁₉×#7596, C₁₉×#7601, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 244);