C₁₉×#7417 #18013376

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7408
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7417

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	AΣL(1,𝔽₁₆)
commutator	C₂×C₄⋊C₄	C₂×C₄×C₁₉
Frattini, cosocle	#384	C₂²×C₁₉
prime radical	C₁₉×#537	C₄
LCS	G ▷ C₂×C₄⋊C₄ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#384 ◁ G

228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 608

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 405);