C₂×C₅×C₁₇×D₄₅ #29505835

order	15300
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×C₁₇×D₄₅
unambiguous semidirect product	(C₂×C₅)⋊(C₅×C₁₇×D₉)
unambiguous semidirect product	(C₂×C₉)⋊(C₅×D₅×C₁₇)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₅×C₁₇
Frattini	C₃	C₂×C₅×C₁₇×D₁₅
Fitting	C₂×C₅²×C₉×C₁₇	C₂
socle	C₂×C₃×C₅²×C₁₇	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₅×C₁₇

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

normal subgroups only

This group has 144 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.

μ_t(G) = 3060

4080 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 221);