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C₂×#72245041 #72245374

order	15552
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₂×C₃

solvable

Aliases

C₂×#72245041

Splittings

C₂×H(5,𝔽₂) ⋊ #6900

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃²	C₃×A₄²
commutator, cosocle	C₃²×H(5,𝔽₂)	C₂×C₃³
Frattini	C₂×C₃²	C₂×C₃×A₄²
Fitting, prime radical	C₂×C₃³×H(5,𝔽₂)	C₃²
hypercenter	C₂²×C₃³	A₄²
hypocenter	H(5,𝔽₂)	C₂×#6900
LCS	G ▷ C₃²×H(5,𝔽₂) ▷ H(5,𝔽₂)
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃³

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1296

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.