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C₄×C₁₃×C₇₉⋊C₉ #49149355

order	36972
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₄×C₁₃×C₇₉⋊C₉

Splittings

derived, Sylow	C₇₉ ⋊ C₄×C₉×C₁₃
Hall	C₄×C₁₃×C₇₉ ⋊ C₉
Hall	C₁₃×C₇₉ ⋊ C₄×C₉
Hall	C₄×C₇₉ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₃	C₇₉⋊C₃
commutator, hypocenter	C₇₉	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₂×C₁₃×C₇₉⋊C₃
Fitting	C₃×C₄×C₁₃×C₇₉	C₃
socle, prime radical	C₂×C₃×C₁₃×C₇₉	C₂×C₃
cosocle	C₂×C₃×C₇₉	C₂×C₃×C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₄×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 36972

Conjugacy classes & character table

4524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 3);