C₁₉×#1348 #14559205

order	2432
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1348

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#102
commutator	C₂×C₈	C₂×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
prime radical	C₂³×C₁₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

116 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1348, C₁₉×#11703, C₁₉×#11704, …
maximal normal subgroup of	C₂×C₁₉×#1348, C₁₉×#11703, C₁₉×#11704, …
maximal quotient of	C₁₉×#7077, C₁₉×#7078, C₁₉×#7089, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 80);