Finite Group Databasebeta

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#120×GL(2,ℤ/4) #72259193

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

#120×GL(2,ℤ/4)

Splittings

C₂⁴×#120 ⋊ D₃

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×S₄
commutator, cosocle	C₂³×A₄	C₂⁵
Fitting	C₂⁴×#120	D₃
socle	C₂⁵	C₂⁴×D₃
hypercenter	C₂²×#120	S₄
hypocenter	A₄	D₄×#120
LCS	G ▷ C₂³×A₄ ▷ A₄
UCS	C₁ ◁ C₂³ ◁ C₂²×#120

At least 6735 conjugacy classes of subgroups; only the 1003 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.