Finite Group Databasebeta

← Prev (#26042596) Next (#26042598) →

C₄×C₁₇×#4296 #26042597

order	11628
isoclinism	isoclinic class of #4296
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

C₄×C₁₇×#4296

Splittings

Fitting, Hall	C₄×C₁₇×C₁₉ ⋊ C₉
derived, Sylow	C₁₉ ⋊ C₄×C₉×C₁₇
Hall	C₁₇×C₁₉ ⋊ C₄×C₉
Hall	C₄×C₁₉ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₁₇	#4296
commutator, hypocenter	C₁₉	C₄×C₉×C₁₇
Frattini	C₂	C₂×C₁₇×#4296
Fitting	C₄×C₁₇×C₁₉	C₉
socle	C₂×C₁₇×C₁₉	C₂×C₉
prime radical	C₂×C₁₇×C₁₉⋊C₃	C₂×C₃
cosocle	C₂×C₁₉⋊C₃	C₂×C₃×C₁₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₁₇

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 45);