Finite Group Databasebeta

← Prev (#22547725) Next (#22547727) →

D₃×C₇×D₉₅ #22547726

order	7980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×D₉₅
unambiguous semidirect product	(C₅×D₃)⋊(C₇×D₁₉)
unambiguous semidirect product	(D₃×C₁₉)⋊(C₇×D₅)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₃×D₉₅
commutator, hypocenter	C₃×C₅×C₁₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₇

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₉×D₉₅, D₃×C₇×C₅⋊(D₁₉⋊C₃), D₃×C₅⋊#11716321, …
maximal normal subgroup of	D₃×C₇×C₅⋊(D₁₉⋊C₃), D₃×C₅⋊#11716321, D₃×C₅⋊#11716322, …
maximal quotient of	C₇×D₉×D₉₅, C₃×D₃×C₇×D₉₅, D₃×C₇×D₂₈₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 151);