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C₉×Dic₁₉₃ #20294265

order	6948
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×Dic₁₉₃

Splittings

derived, Sylow	C₁₉₃ ⋊ C₄×C₉
Hall	C₉×C₁₉₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₉₃
commutator, hypocenter	C₁₉₃	C₄×C₉
Frattini	C₂×C₃	C₃×D₁₉₃
Fitting	C₂×C₉×C₁₉₃	C₂
socle	C₂×C₃×C₁₉₃	C₂×C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₂×C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×Dic₁₉₃, C₉×Dic₉₆₅, C₉×#16838803
maximal normal subgroup of	C₅×C₉×Dic₁₉₃
maximal quotient of	C₅×C₉×Dic₁₉₃, C₉×Dic₉₆₅, C₉×#16838803

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6948, 5);