Finite Group Databasebeta

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C₂×C₃²×D₂₄₇ #22580398

order	8892
isoclinism	isoclinic class of D₂₄₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃²×D₂₄₇

Splittings

Fitting, socle	C₂×C₃²×C₁₃×C₁₉ ⋊ C₂
derived, Hall	C₁₃×C₁₉ ⋊ C₂²×C₃²
Hall	C₃²×C₁₃×C₁₉ ⋊ C₂²
Hall	C₃²×C₁₉ ⋊ C₂×D₁₃
Hall	C₃²×C₁₃ ⋊ C₂×D₁₉
Sylow	C₁₉ ⋊ C₂×C₃²×D₁₃
Sylow	C₁₃ ⋊ C₂×C₃²×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₂₄₇
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃²

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 301);