Finite Group Databasebeta

← Prev (#30683089) Next (#30683091) →

C₂×C₉×D₇×C₆₇ #30683090

order	16884
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₆₇ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₇×C₆₇

Splittings

Fitting	C₂×C₇×C₉×C₆₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₉×C₆₇
Hall	C₇×C₉×C₆₇ ⋊ C₂²
Hall	C₇×C₆₇ ⋊ C₂²×C₉
Hall	C₇×C₉ ⋊ C₂²×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₆₇	D₇
commutator, hypocenter	C₇	C₂²×C₉×C₆₇
Frattini	C₃	C₂×C₃×D₇×C₆₇
Fitting	C₂×C₇×C₉×C₆₇	C₂
socle	C₂×C₃×C₇×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₇×C₆₇	C₃
cosocle	C₃×C₇	C₂²×C₃×C₆₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₆₇

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8442

Conjugacy classes & character table

6030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 59);