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C₃²×D₇×C₆₇ #22554776

order	8442
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₆₇ · Schur multiplier (H₂) = C₃

Aliases

C₃²×D₇×C₆₇

Splittings

Fitting, socle, Hall	C₃²×C₇×C₆₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃²×C₆₇
Hall	C₇×C₆₇ ⋊ C₂×C₃²
Hall	C₃²×C₇ ⋊ C₂×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₆₇	D₇
commutator, hypocenter	C₇	C₂×C₃²×C₆₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₆₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₆₇

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3015 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×D₇×D₆₇, C₃×D₃×D₇×C₆₇, C₃×D₇×D₂₀₁, …
maximal normal subgroup of	C₃²×D₇×D₆₇, C₃×D₃×D₇×C₆₇, C₃×D₇×D₂₀₁, …
maximal quotient of	C₃²×Dic₇×C₆₇, C₂×C₃²×D₇×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 63);