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C₅²×C₂²⋊(C₃₁⋊C₉) #42124577

order	27900
automorphism	?
homology	Abelianization (H₁) = C₅²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×C₂²⋊(C₃₁⋊C₉)
unambiguous semidirect product	C₂²⋊(C₅²×C₃₁⋊C₉)
unambiguous semidirect product	(C₂²×C₅)⋊(C₅×C₃₁⋊C₉)

Splittings

derived, Hall	C₂²×C₃₁ ⋊ C₅²×C₉
Hall	C₂²×C₅²×C₃₁ ⋊ C₉
Hall	C₅²×C₃₁ ⋊ C₂²⋊C₉
Hall	C₂²×C₅² ⋊ C₃₁⋊C₉
Sylow	C₃₁ ⋊ C₅²×C₂²⋊C₉
Sylow	C₂² ⋊ C₅²×C₃₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅²	C₂²⋊(C₃₁⋊C₃)
commutator, hypocenter	C₂²×C₃₁	C₅²×C₉
Frattini	C₃	C₅²×C₂²⋊(C₃₁⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₅²×C₃₁	C₃
cosocle	C₂²×C₃×C₃₁	C₃×C₅²
LCS	G ▷ C₂²×C₃₁
UCS	C₁ ◁ C₃×C₅²

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 324);