D₃×C₃₇×D₇₅ #45685906

order	33300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₃₇×D₇₅
unambiguous semidirect product	(C₃×D₃)⋊(C₃₇×D₂₅)
unambiguous semidirect product	(D₃×C₂₅)⋊(D₃×C₃₇)

	subgroup	G/H
center, hypercenter	C₃₇	D₃×D₇₅
commutator, cosocle, hypocenter	C₃²×C₂₅	C₂²×C₃₇
Frattini	C₅	D₃×D₁₅×C₃₇
Fitting	C₃²×C₂₅×C₃₇	C₂²
socle	C₃²×C₅×C₃₇	C₂×D₅
LCS	G ▷ C₃²×C₂₅
UCS	C₁ ◁ C₃₇

132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

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

μ_t(G) = 5550

4329 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 179);