Finite Group Databasebeta

← Prev (#20301300) Next (#20301302) →

C₇×D₇×C₅²⋊C₃ #20301301

order	7350
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₅

Aliases

C₇×D₇×C₅²⋊C₃

Splittings

Fitting, socle, Hall	C₅²×C₇² ⋊ C₂×C₃
derived	C₅²×C₇ ⋊ C₂×C₃×C₇
Hall	C₇²×C₅²⋊C₃ ⋊ C₂
Hall	C₅²×C₇×D₇ ⋊ C₃
Sylow	C₇² ⋊ C₂×C₅²⋊C₃
Sylow	C₅² ⋊ C₃×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₇×C₅²⋊C₃
commutator, hypocenter	C₅²×C₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₇

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

385 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×D₇×#3874, D₇×C₇⋊#3874, C₇×D₇×(C₅⋊D₅)⋊C₃, …
maximal normal subgroup of	C₇×D₇×#3874, D₇×C₇⋊#3874, C₇×D₇×(C₅⋊D₅)⋊C₃, …
maximal quotient of	C₇×Dic₇×C₅²⋊C₃, C₂×C₇×D₇×C₅²⋊C₃, C₇×D₇×C₅²⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 124);