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C₂₅×D₃₂₃ #30633366

order	16150
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×D₃₂₃
unambiguous semidirect product	C₁₇⋊(C₂₅×D₁₉)
unambiguous semidirect product	C₁₉⋊(C₂₅×D₁₇)

Splittings

Fitting, Hall	C₁₇×C₁₉×C₂₅ ⋊ C₂
derived, Hall	C₁₇×C₁₉ ⋊ C₂×C₂₅
Hall	C₁₉×C₂₅ ⋊ D₁₇
Hall	C₁₇×C₂₅ ⋊ D₁₉
Sylow	C₁₉ ⋊ C₂₅×D₁₇
Sylow	C₁₇ ⋊ C₂₅×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₃₂₃
commutator, hypocenter	C₁₇×C₁₉	C₂×C₂₅
Frattini	C₅	C₅×D₃₂₃
Fitting	C₁₇×C₁₉×C₂₅	C₂
socle, cosocle	C₅×C₁₇×C₁₉	C₂×C₅
prime radical	C₅×D₃₂₃	C₅
LCS	G ▷ C₁₇×C₁₉
UCS	C₁ ◁ C₂₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8075

Conjugacy classes & character table

4075 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₅×D₁₇×D₁₉, D₂₅×D₃₂₃, D₃₂₃⋊D₂₅, …
maximal normal subgroup of	C₂₅×D₁₇×D₁₉, D₂₅×D₃₂₃, D₃₂₃⋊D₂₅, …
maximal quotient of	C₂₅×Dic₃₂₃, C₂×C₂₅×D₃₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16150, 4);