Finite Group Databasebeta

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C₉×D₇×C₁₉₃ #37566508

order	24318
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₉₃

Splittings

Fitting, Hall	C₇×C₉×C₁₉₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₉₃
Hall	C₇×C₁₉₃ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉₃	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₉₃
Frattini	C₃	C₃×D₇×C₁₉₃
Fitting	C₇×C₉×C₁₉₃	C₂
socle	C₃×C₇×C₁₉₃	C₂×C₃
prime radical	C₃×D₇×C₁₉₃	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₉₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₉₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12159

Conjugacy classes & character table

8685 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24318, 7);