C₁₉×H(5,𝔽₃) #17987304

order	4617
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃⁴×C₁₉ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₁₉×H(5,𝔽₃)

Subgroups

	subgroup	G/H
center, socle	C₃×C₁₉	C₃⁴
commutator, Frattini, cosocle	C₃	C₃⁴×C₁₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₉ ◁ G

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 513

A minimal faithful permutation representation — 4 generators on 46 points:

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

Conjugacy classes & character table

1577 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28354980, #28354986, #28355075, …
maximal subgroup of	C₁₉×UT(4,𝔽₃), C₁₉×#10624748, C₁₉×#10624760, …
maximal normal subgroup of	C₁₉×UT(4,𝔽₃), C₁₉×#10624748, C₁₉×#10624760, …
maximal quotient of	C₁₉×#10624862, C₁₉×#10624880, C₁₉×#10624883, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 65);

C19×H(5,𝔽3) #17987304