Finite Group Databasebeta

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C₂×C₉×C₁₇⋊D₁₇ #23780859

order	10404
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₁₇

Aliases

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

Splittings

Fitting	C₂×C₉×C₁₇² ⋊ C₂
derived, Sylow	C₁₇² ⋊ C₂²×C₉
Hall	C₉×C₁₇² ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	C₁₇⋊D₁₇
commutator, hypocenter	C₁₇²	C₂²×C₉
Frattini	C₃	C₂×C₃×C₁₇⋊D₁₇
Fitting	C₂×C₉×C₁₇²	C₂
socle	C₂×C₃×C₁₇²	C₂×C₃
prime radical	C₂×C₃×C₁₇⋊D₁₇	C₃
cosocle	C₃×C₁₇²	C₂²×C₃
LCS	G ▷ C₁₇²
UCS	C₁ ◁ C₂×C₉

300 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 69);