C₁₉×#1379 #14559236

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1379

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	D₄
commutator	C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	C₂²⋊C₈
prime radical	C₂³×C₁₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 136 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 55 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₉×#1379, C₁₉×#12554, C₁₉×#12597, …
maximal normal subgroup of	C₂×C₁₉×#1379, C₁₉×#12554, C₁₉×#12597, …
maximal quotient of	C₁₉×#7141, C₁₉×#7144, C₁₉×#7147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 111);