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C₂×C₉×D₃₄₉ #27160249

order	12564
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₃₄₉

Splittings

Fitting	C₂×C₉×C₃₄₉ ⋊ C₂
derived, Sylow	C₃₄₉ ⋊ C₂²×C₉
Hall	C₉×C₃₄₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₃₄₉
commutator, hypocenter	C₃₄₉	C₂²×C₉
Frattini	C₃	C₂×C₃×D₃₄₉
Fitting	C₂×C₉×C₃₄₉	C₂
socle	C₂×C₃×C₃₄₉	C₂×C₃
prime radical	C₂×C₃×D₃₄₉	C₃
cosocle	C₃×C₃₄₉	C₂²×C₃
LCS	G ▷ C₃₄₉
UCS	C₁ ◁ C₂×C₉

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3168 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12564, 16);