Finite Group Databasebeta

← Prev (#10625293) Next (#10625295) →

C₅×D₃×C₂₅ #10625294

order	750
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₅ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×D₃×C₂₅
unambiguous semidirect product	C₃⋊(C₂×C₅×C₂₅)

Splittings

Fitting, Hall	C₃×C₅×C₂₅ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₅×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₂₅	D₃
commutator, hypocenter	C₃	C₂×C₅×C₂₅
Frattini	C₅	C₅²×D₃
Fitting	C₃×C₅×C₂₅	C₂
socle	C₃×C₅²	C₂×C₅
prime radical	C₅²×D₃	C₅
cosocle	C₃×C₅	C₂×C₅²
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₂₅

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 375

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×D₃×D₂₅, D₃×D₅×C₂₅, D₃×C₅⋊D₂₅, …
maximal normal subgroup of	C₅×D₃×D₂₅, D₃×D₅×C₂₅, D₃×C₅⋊D₂₅, …
maximal quotient of	C₅×Dic₃×C₂₅, C₂×C₅×D₃×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(750, 14);