Finite Group Databasebeta

← Prev (#49149404) Next (#49149406) →

C₂×C₁₃×D₇₉⋊C₉ #49149405

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

Aliases

C₂×C₁₃×D₇₉⋊C₉

Splittings

derived, Sylow	C₇₉ ⋊ C₂²×C₉×C₁₃
Hall	C₁₃×C₇₉⋊C₉ ⋊ C₂²
Hall	C₂×C₁₃×D₇₉ ⋊ C₉
Hall	C₁₃×C₇₉ ⋊ C₂²×C₉
Hall	C₇₉⋊C₉ ⋊ C₂²×C₁₃
Hall	C₂×D₇₉ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₇₉⋊C₃
commutator, hypocenter	C₇₉	C₂²×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×D₇₉⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₂×C₃×C₁₃×D₇₉	C₃
cosocle	C₃×C₇₉	C₂²×C₃×C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₃×C₁₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18486

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 53);