C₁₉×#2164 #14560021

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#2164

Subgroups

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

138 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 96 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)(28,29,31,35,32,36,41,47,33,37,42,48,43,49,53,57)(30,34,39,45,40,46,52,56,38,44,50,54,51,55,58,59);(21,24)(25,27)(28,30)(29,34)(31,39)(32,40)(33,38)(35,45)(36,46)(37,44)(41,52)(42,50)(43,51)(47,56)(48,54)(49,55)(53,58)(57,59);(20,22,23,26)(21,25,24,27)(30,38)(34,44)(39,50)(40,51)(45,54)(46,55)(52,58)(56,59)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₉×#2164, C₁₉×#33419, C₁₉×#33420, …
maximal normal subgroup of	C₂×C₁₉×#2164, C₁₉×#33419, C₁₉×#33420, …
maximal quotient of	C₁₉×#12592, C₁₉×#12600, C₁₉×#12654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 896);