C₁₉×#2239 #14560096

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2238
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2239

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#481
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12299, C₁₉×#12300, C₁₉×#12302, …
maximal normal subgroup of	C₁₉×#12299, C₁₉×#12300, C₁₉×#12302, …
maximal quotient of	C₁₉×#12875, C₁₉×#12931, C₁₉×#13009, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 971);