Finite Group Databasebeta

← Prev (#24925481) Next (#24925483) →

C₂×C₉×D₇×C₄₃ #24925482

order	10836
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₇×C₄₃

Splittings

Fitting	C₂×C₇×C₉×C₄₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₉×C₄₃
Hall	C₇×C₉×C₄₃ ⋊ C₂²
Hall	C₇×C₄₃ ⋊ C₂²×C₉
Hall	C₇×C₉ ⋊ C₂²×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₃	D₇
commutator, hypocenter	C₇	C₂²×C₉×C₄₃
Frattini	C₃	C₂×C₃×D₇×C₄₃
Fitting	C₂×C₇×C₉×C₄₃	C₂
socle	C₂×C₃×C₇×C₄₃	C₂×C₃
prime radical	C₂×C₃×D₇×C₄₃	C₃
cosocle	C₃×C₇	C₂²×C₃×C₄₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₄₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 74);