Finite Group Databasebeta

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D₇×C₂₅×C₃₁ #24925741

order	10850
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₂₅×C₃₁
unambiguous semidirect product	C₇⋊(C₂×C₂₅×C₃₁)

Splittings

Fitting, Hall	C₇×C₂₅×C₃₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₂₅×C₃₁
Hall	C₇×C₃₁ ⋊ C₂×C₂₅
Hall	C₇×C₂₅ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅×C₃₁	D₇
commutator, hypocenter	C₇	C₂×C₂₅×C₃₁
Frattini	C₅	C₅×D₇×C₃₁
Fitting	C₇×C₂₅×C₃₁	C₂
socle	C₅×C₇×C₃₁	C₂×C₅
prime radical	C₅×D₇×C₃₁	C₅
cosocle	C₅×C₇	C₂×C₅×C₃₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₂₅×C₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3875 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×C₂₅×D₃₁, D₇×C₃₁×D₂₅, D₇×D₇₇₅, …
maximal normal subgroup of	D₇×C₂₅×D₃₁, D₇×C₃₁×D₂₅, D₇×D₇₇₅, …
maximal quotient of	C₂₅×Dic₇×C₃₁, C₂×D₇×C₂₅×C₃₁, C₃×D₇×C₂₅×C₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10850, 4);