C₂×C₅²×C₃⋊D₃×C₃₁ #42124991

order	27900
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₃₁ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₂×C₅²×C₃⋊D₃×C₃₁
unambiguous semidirect product	(C₂×C₃)⋊(C₅²×D₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₃₁	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₃₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅²×C₃₁

480 conjugacy classes of subgroups.

9300 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 738);