C₃×C₅×D₅×D₄₉ #28412965

order	14700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₃×C₅×D₅×D₄₉

	subgroup	G/H
center, hypercenter	C₃×C₅	D₅×D₄₉
commutator, cosocle, hypocenter	C₅×C₄₉	C₂²×C₃×C₅
Frattini	C₇	C₃×C₅×D₅×D₇
Fitting	C₃×C₅²×C₄₉	C₂²
socle	C₃×C₅²×C₇	C₂×D₇
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₃×C₅

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

1560 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 144);