Finite Group Databasebeta

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C₇×C₈×C₉×Dic₃ #72219185

order	6048
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₈×C₉ · Schur multiplier (H₂) = C₄

Aliases

C₇×C₈×C₉×Dic₃

Splittings

derived	C₃ ⋊ C₄×C₇×C₈×C₉
Hall	C₃×C₇×C₉ ⋊ C₄×C₈
Sylow	C₃×C₉ ⋊ C₄×C₇×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇×C₈×C₉	D₃
commutator, hypocenter	C₃	C₄×C₇×C₈×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₃×C₇
Fitting	C₂×C₃×C₇×C₈×C₉	C₂
socle, prime radical	C₂²×C₃²×C₇	C₂×C₃×C₄
cosocle	C₂×C₃²×C₄	C₂²×C₃×C₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇×C₈×C₉

308 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×D₃×C₇×C₈×C₉
maximal normal subgroup of	C₄×D₃×C₇×C₈×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.