Finite Group Databasebeta

← Prev (#26015248) Next (#26015250) →

C₉×D₁₇×C₃₇ #26015249

order	11322
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₇×C₃₇
unambiguous semidirect product	C₁₇⋊(C₂×C₉×C₃₇)

Splittings

Fitting, Hall	C₉×C₁₇×C₃₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₉×C₃₇
Hall	C₁₇×C₃₇ ⋊ C₂×C₉
Hall	C₉×C₁₇ ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₇	D₁₇
commutator, hypocenter	C₁₇	C₂×C₉×C₃₇
Frattini	C₃	C₃×D₁₇×C₃₇
Fitting	C₉×C₁₇×C₃₇	C₂
socle	C₃×C₁₇×C₃₇	C₂×C₃
prime radical	C₃×D₁₇×C₃₇	C₃
cosocle	C₃×C₁₇	C₂×C₃×C₃₇
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₉×C₃₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₃₇×#595, C₉×#14578981, C₉×D₁₇×D₃₇, …
maximal normal subgroup of	C₉×C₃₇×#595, C₉×#14578981, C₉×D₁₇×D₃₇, …
maximal quotient of	C₉×C₃₇×Dic₁₇, C₂×C₉×D₁₇×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11322, 4);