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C₁₉×C₃⋊(C₃⋊(C₇⋊Dic₇)) #45691960

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₃×C₇

Aliases

direct product	C₁₉×C₃⋊(C₃⋊(C₇⋊Dic₇))
unambiguous semidirect product	C₃⋊(C₁₉×C₃⋊(C₇⋊Dic₇))
unambiguous semidirect product	C₇⋊(C₁₉×C₃⋊Dic₂₁)

Splittings

derived, Hall	C₃²×C₇² ⋊ C₄×C₁₉
Hall	C₃²×C₇²×C₁₉ ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃⋊Dic₃
Hall	C₃²×C₁₉ ⋊ C₇⋊Dic₇
Sylow	C₇² ⋊ C₁₉×C₃⋊Dic₃
Sylow	C₃² ⋊ C₁₉×C₇⋊Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊(C₃⋊(C₇⋊D₇))
commutator, hypocenter	C₃²×C₇²	C₄×C₁₉
Frattini	C₂	C₁₉×C₃⋊(C₃⋊(C₇⋊D₇))
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃²×C₇²	C₂×C₁₉
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₂×C₁₉

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33516

Conjugacy classes & character table

8436 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 758);