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C₄₇×Dic₁₃⋊C₉ #36347170

order	21996
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₇×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₄₇)
unambiguous semidirect product	(C₄₇×Dic₁₃)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₄₇
Hall	C₄₇×C₁₃⋊C₉ ⋊ C₄
Hall	C₄₇×Dic₁₃ ⋊ C₉
Hall	C₁₃×C₄₇ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₄₇
Hall	Dic₁₃ ⋊ C₉×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₄₇
Frattini	C₂×C₃	C₄₇×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₄₇	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₄₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄₇

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 21996

Conjugacy classes & character table

2256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 11);