C₁₉×#1515 #14559372

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×#1515

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	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 208 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) = 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)(21,26,28,40)(22,31)(23,35)(27,42,43,51)(29,41,30,36)(33,48)(34,47)(37,38)(39,44,50,45)(46,49);(20,21,24,29)(22,27,34,44)(23,36,35,40)(25,30,32,28)(26,38,41,37)(31,45,47,43)(33,42,49,50)(39,48,51,46);(20,22,32,47)(21,27,28,43)(23,33,38,48)(24,34,25,31)(26,39,40,50)(29,44,30,45)(35,49,37,46)(36,42,41,51)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8501, C₁₉×#8502, C₁₉×#8503, …
maximal normal subgroup of	C₁₉×#8501, C₁₉×#8502, C₁₉×#8503, …
maximal quotient of	C₁₉×#7596, C₁₉×#7604, C₁₉×#7605, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 247);