C₁₉×#3363 #14561220

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3363

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ G

336 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 2432

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#19812, C₁₉×#19816, C₁₉×#19817, …
maximal normal subgroup of	C₁₉×#19812, C₁₉×#19816, C₁₉×#19817, …
maximal quotient of	Q₈×C₁₉×#103, C₁₉×#22542, C₁₉×#22740, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2095);