C₁₉×#3292 #14561149

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#3292

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ G

476 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12310, C₁₉×#12312, C₁₉×#12366, …
maximal normal subgroup of	C₁₉×#12310, C₁₉×#12312, C₁₉×#12366, …
maximal quotient of	C₁₉×#19885, C₁₉×#19893, C₁₉×#19898, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2024);