Finite Group Databasebeta

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C₂×D₃×#12705 #72254083

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹²

Aliases

C₂×D₃×#12705

Splittings

Fitting	C₂×C₃×#12705 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#12705

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1781
commutator	C₂⁴×C₃	C₂⁴×C₄
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#12705	C₂
socle	C₂²×C₃	C₂×#1781
prime radical	C₂×D₃×#3484	C₂
cosocle	C₂²×C₃×D₄	C₂⁵
hypercenter	C₂×#12705	D₃
hypocenter	C₃	C₂²×#12705
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ C₂×#12705

At least 9750 conjugacy classes of subgroups; only the 2279 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#511790, D₃×#72219159, D₃×#72219158
maximal normal subgroup of	C₂×D₃×#511790, D₃×#72219159, D₃×#72219158

GAP

Past the SmallGroups library coverage — no SmallGroups id.