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C₂²×C₁₉×#89205 #45691699

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

Aliases

C₂²×C₁₉×#89205

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₁₉	#3862
commutator, hypocenter	C₇²	C₂²×C₉×C₁₉
Frattini	C₃	C₂²×C₁₉×#3862
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₉	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²×C₃×C₁₉

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

4332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 497);