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#4296⋊AGL(1,𝔽₅) #16811873

order	3420
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product

#4296⋊AGL(1,𝔽₅)

Splittings

Fitting, socle, derived, Hall	C₅×C₁₉ ⋊ C₄×C₉
Hall	C₅×#4296 ⋊ C₄
Hall	C₁₉⋊AGL(1,𝔽₅) ⋊ C₉
Hall	#4296 ⋊ AGL(1,𝔽₅)
Sylow	C₁₉ ⋊ C₉×AGL(1,𝔽₅)
Sylow	C₅ ⋊ #4296⋊C₄

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉	C₄×C₉
prime radical, cosocle	D₅×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 95

Polycyclic presentation:

2,3,2,3,5,19|a^2=c,b^3=d,e^a=e^2,f^a=f^18,f^b=f^4,e^c=e^4,f^d=f^7

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#4296⋊#1035, C₅×#4296⋊AGL(1,𝔽₅), #4296⋊#1043, …
maximal normal subgroup of	C₅×#4296⋊AGL(1,𝔽₅), C₇×#4296⋊AGL(1,𝔽₅), C₁₁×#4296⋊AGL(1,𝔽₅), …
maximal quotient of	#4296⋊#1035, C₅×#4296⋊AGL(1,𝔽₅), #4296⋊#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3420, 66);