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C₂×C₉×D₁₃×C₇₉ #49149442

order	36972
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₁₃×C₇₉

Splittings

Fitting	C₂×C₉×C₁₃×C₇₉ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂²×C₉×C₇₉
Hall	C₉×C₁₃×C₇₉ ⋊ C₂²
Hall	C₁₃×C₇₉ ⋊ C₂²×C₉
Hall	C₉×C₁₃ ⋊ C₂²×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₇₉	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₇₉
Frattini	C₃	C₂×C₃×D₁₃×C₇₉
Fitting	C₂×C₉×C₁₃×C₇₉	C₂
socle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₂×C₃×D₁₃×C₇₉	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₇₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₇₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18486

Conjugacy classes & character table

11376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 90);