Finite Group Databasebeta

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C₂²×C₁₇×#4294 #26042583

order	11628
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₇×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₂²×C₉×C₁₇
Hall	C₂²×C₁₇×C₁₉ ⋊ C₉
Hall	C₁₇×C₁₉ ⋊ C₂²×C₉
Hall	C₂²×C₁₉ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₁₇	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₉×C₁₇
Frattini	C₃	C₂²×C₁₇×C₁₉⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₁₇×C₁₉	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₁₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₁₇

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 31);