C₁₉×#7426 #18013385

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7426
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7426

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1351
commutator	C₂×C₂²⋊C₄	C₂×C₄×C₁₉
Frattini, cosocle	#379	C₂²×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₁₉×#379 ◁ G

332 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 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)(22,28)(23,31)(24,27)(25,29,34,32)(26,33)(30,35);(20,22)(21,25)(23,32,33,29)(24,30)(26,28,31,35)(27,34)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 414);