Finite Group Databasebeta

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C₉×D₇×C₁₉₇ #37613898

order	24822
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉₇ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₉₇

Splittings

Fitting, Hall	C₇×C₉×C₁₉₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₉₇
Hall	C₇×C₁₉₇ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉₇	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₉₇
Frattini	C₃	C₃×D₇×C₁₉₇
Fitting	C₇×C₉×C₁₉₇	C₂
socle	C₃×C₇×C₁₉₇	C₂×C₃
prime radical	C₃×D₇×C₁₉₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₉₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₉₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12411

Conjugacy classes & character table

8865 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24822, 5);