C₃×(C₅⋊(D₃₇⋊C₃))⋊D₅ #45686232

order	33300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×(C₅⋊(D₃₇⋊C₃))⋊D₅
unambiguous semidirect product	(C₅⋊(D₃₇⋊C₃))⋊(C₃×D₅)
unambiguous semidirect product	((C₅⋊D₅)⋊D₃₇)⋊C₃²
unambiguous semidirect product	(C₃×(C₅⋊D₅)⋊D₃₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₃	(C₅⋊(D₃₇⋊C₃))⋊D₅
commutator, cosocle, hypocenter	C₅²×C₃₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₇	C₂²×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₃

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

μ_t(G) = 1110

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 505);