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C₉×(C₇⋊D₇)⋊D₁₉ #45691665

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×(C₇⋊D₇)⋊D₁₉

Splittings

Fitting, Hall	C₇²×C₉×C₁₉ ⋊ C₂²
derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₉
Hall	C₇²×C₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ D₇²
Sylow	C₇² ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₉×D₇²

Subgroups

	subgroup	G/H
center, hypercenter	C₉	(C₇⋊D₇)⋊D₁₉
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₃×(C₇⋊D₇)⋊D₁₉
Fitting	C₇²×C₉×C₁₉	C₂²
socle, cosocle	C₃×C₇²×C₁₉	C₂²×C₃
prime radical	C₃×(C₇⋊D₇)⋊D₁₉	C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₉

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

2331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 463);