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C₇²×Dic₁₇₁ #45691533

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇²×Dic₁₇₁
unambiguous semidirect product	C₉⋊(C₇²×Dic₁₉)
unambiguous semidirect product	C₁₉⋊(C₇²×Dic₉)

Splittings

derived, Hall	C₉×C₁₉ ⋊ C₄×C₇²
Hall	C₇²×C₉×C₁₉ ⋊ C₄
Hall	C₇²×C₁₉ ⋊ Dic₉
Hall	C₇²×C₉ ⋊ Dic₁₉
Sylow	C₁₉ ⋊ C₇²×Dic₉
Sylow	C₉ ⋊ C₇²×Dic₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₄×C₇²
Frattini	C₂×C₃	C₇²×D₅₇
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₉	D₃
cosocle	C₂×C₉×C₁₉	C₂×C₇²
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₇²

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33516

Conjugacy classes & character table

8526 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 331);