Finite Group Databasebeta

← Prev (#22551288) Next (#22551290) →

C₃²×C₅×C₁₃×D₇ #22551289

order	8190
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₅×C₁₃×D₇

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₅×C₁₃	D₇
commutator, hypocenter	C₇	C₂×C₃²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₅×C₁₃

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₅×D₇×D₁₃, C₃²×D₅×C₁₃×D₇, C₃²×D₇×D₆₅, …
maximal normal subgroup of	C₃²×C₅×D₇×D₁₃, C₃²×D₅×C₁₃×D₇, C₃²×D₇×D₆₅, …
maximal quotient of	C₃²×C₅×C₁₃×Dic₇, C₂×C₃²×C₅×C₁₃×D₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 123);