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C₇₁×Dic₁₃⋊C₉ #45684875

order	33228
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₁×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₇₁)
unambiguous semidirect product	(Dic₁₃×C₇₁)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₇₁
Hall	C₇₁×C₁₃⋊C₉ ⋊ C₄
Hall	Dic₁₃×C₇₁ ⋊ C₉
Hall	C₁₃×C₇₁ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₇₁
Hall	Dic₁₃ ⋊ C₉×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇₁	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₇₁
Frattini	C₂×C₃	C₇₁×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₇₁	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₇₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₇₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33228

Conjugacy classes & character table

3408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33228, 11);