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#13083980

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Hall	C₅×C₉ ⋊ #108
Sylow	C₉ ⋊ #3996
Sylow	C₅ ⋊ #63372

Subgroups

	subgroup	G/H
center	C₂	C₄⋊(C₉⋊AGL(1,𝔽₅))
commutator	C₄×C₅×C₉	C₂×C₄
Frattini	C₃×C₄	C₂×ΓL(1,𝔽₁₆)
Fitting	C₅×C₈×C₉	C₄
socle	C₂×C₃×C₅	C₄⋊Dic₃
prime radical	C₂×C₃×D₅	Dic₆
cosocle	C₄×C₉×D₅	C₂²
hypercenter	C₈	C₉⋊AGL(1,𝔽₅)
hypocenter	C₅×C₉	#108
LCS	G ▷ C₄×C₅×C₉ ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 720

Polycyclic presentation:

2^5,3,5,3|a^2=c,b^2=de,c^2=e,d^2=e,f^3=h,b^a=bd,d^a=de,f^a=f^2h^2,g^a=g^2,h^a=h^2,g^c=g^4

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 297);