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C₁₇×D₁₀₃⋊C₉ #44538547

order	31518
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₁₀₃⋊C₉
unambiguous semidirect product	(C₁₇×D₁₀₃)⋊C₉

Splittings

derived, Sylow	C₁₀₃ ⋊ C₂×C₉×C₁₇
Hall	C₁₇×C₁₀₃⋊C₉ ⋊ C₂
Hall	C₁₇×D₁₀₃ ⋊ C₉
Hall	C₁₇×C₁₀₃ ⋊ C₂×C₉
Hall	C₁₀₃⋊C₉ ⋊ C₂×C₁₇
Hall	D₁₀₃ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₁₀₃⋊C₃
commutator, hypocenter	C₁₀₃	C₂×C₉×C₁₇
Frattini	C₃	C₁₇×D₁₀₃⋊C₃
Fitting, socle	C₃×C₁₇×C₁₀₃	C₂×C₃
prime radical	C₃×C₁₇×D₁₀₃	C₃
cosocle	C₃×C₁₀₃	C₂×C₃×C₁₇
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₃×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15759

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31518, 15);