Finite Group Databasebeta

← Prev (#23756017) Next (#23756019) →

C₁₉×ΓL(1,𝔽₈)×C₂₅ #23756018

order	9975
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×ΓL(1,𝔽₈)×C₂₅
unambiguous semidirect product	C₇⋊(C₃×C₁₉×C₂₅)
unambiguous semidirect product	(C₇×C₂₅)⋊(C₃×C₁₉)

Splittings

Fitting, Hall	C₇×C₁₉×C₂₅ ⋊ C₃
derived, Sylow	C₇ ⋊ C₃×C₁₉×C₂₅
Hall	C₇×C₂₅ ⋊ C₃×C₁₉
Hall	C₇×C₁₉ ⋊ C₃×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₂₅	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₃×C₁₉×C₂₅
Frattini	C₅	C₅×C₁₉×ΓL(1,𝔽₈)
Fitting	C₇×C₁₉×C₂₅	C₃
socle	C₅×C₇×C₁₉	C₃×C₅
prime radical	C₅×C₁₉×ΓL(1,𝔽₈)	C₅
cosocle	C₅×C₇	C₃×C₅×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₉×C₂₅

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2375 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₉×ΓL(1,𝔽₈)×C₂₅, ΓL(1,𝔽₈)×C₂₅×D₁₉, C₁₉×C₂₅×AGL(1,𝔽₇), …
maximal normal subgroup of	C₂×C₁₉×ΓL(1,𝔽₈)×C₂₅, ΓL(1,𝔽₈)×C₂₅×D₁₉, C₁₉×C₂₅×AGL(1,𝔽₇), …
maximal quotient of	C₂×C₁₉×ΓL(1,𝔽₈)×C₂₅, C₁₉×C₂₅×C₇⋊C₉, C₃×C₁₉×ΓL(1,𝔽₈)×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9975, 3);