Finite Group Databasebeta

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C₉×D₁₃×C₃₇ #22575855

order	8658
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₃×C₃₇

Splittings

Fitting, Hall	C₉×C₁₃×C₃₇ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₉×C₃₇
Hall	C₁₃×C₃₇ ⋊ C₂×C₉
Hall	C₉×C₁₃ ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₇	D₁₃
commutator, hypocenter	C₁₃	C₂×C₉×C₃₇
Frattini	C₃	C₃×D₁₃×C₃₇
Fitting	C₉×C₁₃×C₃₇	C₂
socle	C₃×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₉×C₃₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2664 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₃₇×#261, C₉×#14515322, C₉×D₁₃×D₃₇, …
maximal normal subgroup of	C₉×C₃₇×#261, C₉×#14515322, C₉×D₁₃×D₃₇, …
maximal quotient of	C₉×C₃₇×Dic₁₃, C₂×C₉×D₁₃×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8658, 7);