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C₂×C₉×C₁₉×C₇⋊D₇ #45691714

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂×C₇

Aliases

C₂×C₉×C₁₉×C₇⋊D₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	C₇⋊D₇
commutator, hypocenter	C₇²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×C₇⋊D₇
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₉×C₁₉

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16758

Conjugacy classes & character table

8892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 512);