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C₁₇×C₁₉×#1044 #44568113

order	32300
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

C₁₇×C₁₉×#1044

Splittings

Fitting, socle, Hall	C₅²×C₁₇×C₁₉ ⋊ C₄
derived, Sylow	C₅² ⋊ C₄×C₁₇×C₁₉
Hall	C₅²×C₁₉ ⋊ C₄×C₁₇
Hall	C₅²×C₁₇ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₁₉	#1044
commutator, hypocenter	C₅²	C₄×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₁₉	C₄
prime radical	C₁₇×C₁₉×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₁₇×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₇×C₁₉

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3230

Conjugacy classes & character table

3230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 102);