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C₁₇×C₁₉×Dic₂₅ #44568016

order	32300
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₇×C₁₉×Dic₂₅

Splittings

derived, Sylow	C₂₅ ⋊ C₄×C₁₇×C₁₉
Hall	C₁₇×C₁₉×C₂₅ ⋊ C₄
Hall	C₁₉×C₂₅ ⋊ C₄×C₁₇
Hall	C₁₇×C₂₅ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇×C₁₉	D₂₅
commutator, hypocenter	C₂₅	C₄×C₁₇×C₁₉
Frattini	C₂×C₅	D₅×C₁₇×C₁₉
Fitting	C₂×C₁₇×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₇×C₁₉	D₅
cosocle	C₂×C₂₅	C₂×C₁₇×C₁₉
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₁₇×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32300

Conjugacy classes & character table

9044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 5);