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C₂²×C₉×C₇₉⋊C₁₃ #49149392

order	36972
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂²×C₉×C₇₉⋊C₁₃
unambiguous semidirect product	(C₂²×C₉×C₇₉)⋊C₁₃

Splittings

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

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2844

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 40);