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C₄₉×(C₃⋊D₃)⋊D₁₃ #37524289

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄₉×(C₃⋊D₃)⋊D₁₃
unambiguous semidirect product	(C₃⋊D₃)⋊(D₁₃×C₄₉)
unambiguous semidirect product	D₃₉⋊(D₃×C₄₉)

Splittings

Fitting, Hall	C₃²×C₁₃×C₄₉ ⋊ C₂²
derived, Hall	C₃²×C₁₃ ⋊ C₂²×C₄₉
Hall	C₁₃×C₄₉ ⋊ D₃²
Hall	C₃²×C₄₉ ⋊ C₂×D₁₃
Sylow	C₁₃ ⋊ D₃²×C₄₉
Sylow	C₃² ⋊ C₂×D₁₃×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉	(C₃⋊D₃)⋊D₁₃
commutator, hypocenter	C₃²×C₁₃	C₂²×C₄₉
Frattini	C₇	C₇×(C₃⋊D₃)⋊D₁₃
Fitting	C₃²×C₁₃×C₄₉	C₂²
socle, cosocle	C₃²×C₇×C₁₃	C₂²×C₇
prime radical	C₇×(C₃⋊D₃)⋊D₁₃	C₇
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₄₉

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3822

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 234);