Finite Group Databasebeta

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C₂×C₉×D₇×C₇₁ #31822022

order	17892
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₇×C₇₁

Splittings

Fitting	C₂×C₇×C₉×C₇₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₉×C₇₁
Hall	C₇×C₉×C₇₁ ⋊ C₂²
Hall	C₇×C₇₁ ⋊ C₂²×C₉
Hall	C₇×C₉ ⋊ C₂²×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₇₁	D₇
commutator, hypocenter	C₇	C₂²×C₉×C₇₁
Frattini	C₃	C₂×C₃×D₇×C₇₁
Fitting	C₂×C₇×C₉×C₇₁	C₂
socle	C₂×C₃×C₇×C₇₁	C₂×C₃
prime radical	C₂×C₃×D₇×C₇₁	C₃
cosocle	C₃×C₇	C₂²×C₃×C₇₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₇₁

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8946

Conjugacy classes & character table

6390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 39);