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C₄₉×Dic₁₃⋊C₉ #37524057

order	22932
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₉×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₄₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₄₉
Hall	C₄₉×C₁₃⋊C₉ ⋊ C₄
Hall	C₄₉×Dic₁₃ ⋊ C₉
Hall	C₁₃×C₄₉ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₄₉
Hall	Dic₁₃ ⋊ C₉×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₉	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₄₉
Frattini	C₂×C₃×C₇	C₇×D₁₃⋊C₃
Fitting	C₂×C₃×C₁₃×C₄₉	C₂×C₃
socle, prime radical, cosocle	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄₉

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22932

Conjugacy classes & character table

2352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 2);