C₃×D₅×C₅⋊(D₃₇⋊C₃) #45686231

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

Aliases

direct product	C₃×D₅×C₅⋊(D₃₇⋊C₃)
unambiguous semidirect product	(C₅×D₅)⋊(C₃×D₃₇⋊C₃)
unambiguous semidirect product	(D₅×C₃₇⋊C₃)⋊(C₃×D₅)
unambiguous semidirect product	(D₅×D₁₈₅)⋊C₃²
unambiguous semidirect product	(C₃×D₅×D₁₈₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₃	D₅×C₅⋊(D₃₇⋊C₃)
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 72 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

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

μ_t(G) = 1110

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 504);