C₁₉×#7316 #18013275

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7316
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#7316

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1304
commutator	C₂⁴	C₄²×C₁₉
Frattini, cosocle	C₂³×D₄	C₂²×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

620 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 74 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)(20,21,23,26)(22,28,29,34)(24,27,32,35)(25,31,33,30);(20,22)(21,25,27,28)(23,31,32,29)(24,30)(26,34)(33,35)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 304);