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C₃×Dic₇×C₈₉ #21418756

order	7476
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₇×C₈₉

Splittings

derived, Sylow	C₇ ⋊ C₃×C₄×C₈₉
Hall	C₃×C₇×C₈₉ ⋊ C₄
Hall	C₇×C₈₉ ⋊ C₃×C₄
Hall	C₃×C₇ ⋊ C₄×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈₉	D₇
commutator, hypocenter	C₇	C₃×C₄×C₈₉
Frattini	C₂	C₃×D₇×C₈₉
Fitting, socle	C₂×C₃×C₇×C₈₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2670 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×Dic₇×C₈₉, C₈₉×Dic₇⋊C₉, C₃×ΓL(1,𝔽₈)⋊C₄×C₈₉, …
maximal normal subgroup of	C₉×Dic₇×C₈₉, C₈₉×Dic₇⋊C₉, C₃×ΓL(1,𝔽₈)⋊C₄×C₈₉, …
maximal quotient of	C₉×Dic₇×C₈₉, C₃×Dic₂₁×C₈₉, C₃²×Dic₇×C₈₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7476, 4);