C₁₉×#7481 #18013440

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#7481

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1390
commutator	C₂×Q₈	C₄²×C₁₉
Frattini, cosocle	C₂×#124	C₂²×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#124 ◁ G

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30,32,46)(23,35,36,45)(24,38,40,29)(25,28)(26,31,41,49)(27,37)(33,48,34,47)(39,44)(42,50,43,51);(20,22)(21,26,28,42)(23,31)(24,32)(25,34)(27,30,44,47)(29,41,38,43)(33,40)(35,46,45,48)(36,50)(37,51)(39,49)

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, 469);