Finite Group Databasebeta

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C₅²×C₁₉×Dic₁₇ #44568057

order	32300
automorphism	?
homology	Abelianization (H₁) = C₄×C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

C₅²×C₁₉×Dic₁₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₉	D₁₇
commutator, hypocenter	C₁₇	C₄×C₅²×C₁₉
Frattini	C₂	C₅²×C₁₉×D₁₇
Fitting, socle, prime radical	C₂×C₅²×C₁₇×C₁₉	C₂
cosocle	C₂×C₁₇	C₂×C₅²×C₁₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₅²×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32300

Conjugacy classes & character table

9500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 46);