C₁₉×#2901 #14560758

order	2432
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#2901

Subgroups

	subgroup	G/H
center	C₄×C₁₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₁₉×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

738 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 340 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)(20,21,24,28,25,22,29,27)(23,26,32,34,31,30,35,33);(20,22)(21,25)(23,30)(24,27)(26,31)(28,29)(32,33)(34,35);(20,23)(21,26)(22,30)(24,32)(25,31)(27,33)(28,34)(29,35);(23,31)(26,30)(32,35)(33,34)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#22461, C₁₉×#22462, C₁₉×#22898, …
maximal normal subgroup of	C₁₉×#22461, C₁₉×#22462, C₁₉×#22898, …
maximal quotient of	C₁₉×#17438, C₁₉×#17439, C₁₉×#17453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1633);