C₁₉×#2242 #14560099

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#2242

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×D₈×C₁₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,42)(31,36)(32,50)(33,53)(34,54)(35,41)(37,46)(38,43)(39,52)(40,51)(44,56)(45,55)(47,59)(48,58)(49,57);(21,24)(25,27)(28,30,43,48,34,45,52,49,35,46,33,44,51,47,32,31)(29,36,50,59,40,56,53,37,41,57,39,55,54,58,38,42);(20,22,23,26)(21,25,24,27)(28,31,32,47,51,44,33,46,35,49,52,45,34,48,43,30)(29,37,38,56,54,59,39,36,41,42,53,58,40,55,50,57)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2242, C₁₉×#33697, C₁₉×#33702, …
maximal normal subgroup of	C₂×C₁₉×#2242, C₁₉×#33697, C₁₉×#33702, …
maximal quotient of	C₁₉×#12889, C₁₉×#13147, C₁₉×#13148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 974);