C₂×C₅²×C₁₃×C₃⋊D₃ #26043872

order	11700
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₁₃ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₂×C₅²×C₁₃×C₃⋊D₃
unambiguous semidirect product	(C₂×C₃)⋊(C₅²×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅²×C₁₃

480 conjugacy classes of subgroups.

3900 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 719);