Finite Group Databasebeta

← Prev (#45657378) Next (#45657380) →

C₇×C₉×D₇×C₃₇ #45657379

order	32634
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

C₇×C₉×D₇×C₃₇

Splittings

Fitting, Hall	C₇²×C₉×C₃₇ ⋊ C₂
derived	C₇ ⋊ C₂×C₇×C₉×C₃₇
Hall	C₇²×C₃₇ ⋊ C₂×C₉
Hall	C₇²×C₉ ⋊ C₂×C₃₇
Sylow	C₇² ⋊ C₂×C₉×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉×C₃₇	D₇
commutator, hypocenter	C₇	C₂×C₇×C₉×C₃₇
Frattini	C₃	C₃×C₇×D₇×C₃₇
Fitting	C₇²×C₉×C₃₇	C₂
socle	C₃×C₇²×C₃₇	C₂×C₃
prime radical	C₃×C₇×D₇×C₃₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₇×C₃₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₇×C₉×C₃₇

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4662

Conjugacy classes & character table

11655 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32634, 159);