C₅×C₃₁×(C₃⋊D₃)⋊D₅ #42124930

order	27900
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₃₁×(C₃⋊D₃)⋊D₅
unambiguous semidirect product	(C₃⋊D₃)⋊(C₅×D₅×C₃₁)
unambiguous semidirect product	D₁₅⋊(C₅×D₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₅×C₃₁	(C₃⋊D₃)⋊D₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₃₁	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₃₁

224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

3255 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 677);