C₅×D₁₅⋊D₁₁₉ #49087952

order	35700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₁₅⋊D₁₁₉
unambiguous semidirect product	D₁₅⋊(C₅×D₁₁₉)

	subgroup	G/H
center, hypercenter	C₅	D₁₅⋊D₁₁₉
commutator, cosocle, hypocenter	C₃×C₅×C₇×C₁₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₅×C₇×C₁₇
UCS	C₁ ◁ C₅

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 3570

2715 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 426);