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C₅×C₁₉×Dic₈₅ #44568053

order	32300
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₁₉×Dic₈₅

Splittings

derived	C₅×C₁₇ ⋊ C₄×C₅×C₁₉
Hall	C₅²×C₁₇×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ Dic₁₇
Hall	C₅²×C₁₇ ⋊ C₄×C₁₉
Hall	C₁₇×C₁₉ ⋊ C₅×Dic₅
Sylow	C₅² ⋊ C₁₉×Dic₁₇
Sylow	C₁₇ ⋊ C₅×C₁₉×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₈₅
commutator, hypocenter	C₅×C₁₇	C₄×C₅×C₁₉
Frattini	C₂	C₅×C₁₉×D₈₅
Fitting, socle, prime radical	C₂×C₅²×C₁₇×C₁₉	C₂
cosocle	C₂×C₅×C₁₇	C₂×C₅×C₁₉
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂×C₅×C₁₉

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6460

Conjugacy classes & character table

8360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 42);