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C₁₉×C₂₅×Dic₁₇ #44568014

order	32300
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×C₂₅×Dic₁₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₅	D₁₇
commutator, hypocenter	C₁₇	C₄×C₁₉×C₂₅
Frattini	C₂×C₅	C₅×C₁₉×D₁₇
Fitting	C₂×C₁₇×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₇×C₁₉	C₂×C₅
cosocle	C₂×C₅×C₁₇	C₂×C₅×C₁₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₉×C₂₅

36 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, 3);