Finite Group Databasebeta

← Prev (#36347801) Next (#36347803) →

C₅×C₇⋊C₉×D₃₅ #36347802

order	22050
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇⋊C₉×D₃₅
unambiguous semidirect product	C₅⋊(C₅×D₇×C₇⋊C₉)

Splittings

derived	C₅×C₇² ⋊ C₂×C₅×C₉
Hall	C₅²×C₇×C₇⋊C₉ ⋊ C₂
Hall	C₅×C₇×D₃₅ ⋊ C₉
Hall	C₅²×C₇² ⋊ C₂×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₅×D₅
Sylow	C₇² ⋊ C₅×C₉×D₅
Sylow	C₅² ⋊ D₇×C₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅	ΓL(1,𝔽₈)×D₃₅
commutator, hypocenter	C₅×C₇²	C₂×C₅×C₉
Frattini	C₃	C₅×ΓL(1,𝔽₈)×D₃₅
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
prime radical	C₃×C₅×C₇×D₃₅	C₃
cosocle	C₃×C₅×C₇²	C₂×C₃×C₅
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₃×C₅

136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 630

Conjugacy classes & character table

1425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 239);