C₁₉×#7348 #18013307

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7348
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7348

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1317
commutator	C₂²×C₄	C₂×C₈×C₁₉
Frattini, cosocle	#381	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₁₉×#381 ◁ G

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

normal subgroups only

This group has 200 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) = 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)(20,21,24,28)(22,30,32,46,33,47,49,51)(23,34,35,44)(25,29,37,45)(26,38,39,48,40,50,43,31)(27,41,42,36);(20,22)(21,26,29,40)(23,31)(24,32)(25,33)(27,30,34,47)(28,43,45,39)(35,38)(36,48)(37,49)(41,50)(42,51,44,46)

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, 336);