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C₂×#11720574 #13144806

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×#11720574

Splittings

H(3,𝔽₃) ⋊ C₂×#95

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂×C₃⋊D₃
commutator	C₂×H(3,𝔽₃)	C₂×C₄²
Frattini	C₂³×C₃	C₂²×C₃⋊D₃
Fitting	C₂³×C₄×H(3,𝔽₃)	C₂
prime radical	C₂⁴×H(3,𝔽₃)	C₂²
cosocle	C₂³×H(3,𝔽₃)	C₂³
hypercenter	C₂³×C₃×C₄	C₃⋊D₃
hypocenter	H(3,𝔽₃)	C₂×#95
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂³×C₃×C₄

1815 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10869);