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C₃²×D₇×C₅₉ #21418285

order	7434
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅₉ · Schur multiplier (H₂) = C₃

Aliases

C₃²×D₇×C₅₉

Splittings

Fitting, socle, Hall	C₃²×C₇×C₅₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃²×C₅₉
Hall	C₇×C₅₉ ⋊ C₂×C₃²
Hall	C₃²×C₇ ⋊ C₂×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₅₉	D₇
commutator, hypocenter	C₇	C₂×C₃²×C₅₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₅₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₅₉

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2655 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×D₇×D₅₉, C₃×D₃×D₇×C₅₉, C₃×D₇×D₁₇₇, …
maximal normal subgroup of	C₃²×D₇×D₅₉, C₃×D₃×D₇×C₅₉, C₃×D₇×D₁₇₇, …
maximal quotient of	C₃²×Dic₇×C₅₉, C₂×C₃²×D₇×C₅₉, C₃²×C₅×D₇×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7434, 23);