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C₉×C₁₉×Dic₃₅ #37560879

order	23940
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×Dic₃₅

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₃₅
commutator, hypocenter	C₅×C₇	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×C₁₉×D₃₅
Fitting	C₂×C₅×C₇×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₅×C₇	C₂×C₃×C₁₉
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₉×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 23940

Conjugacy classes & character table

6498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 11);