C₇×C₁₇×D₁₅⋊D₅ #49087985

order	35700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₁₇×D₁₅⋊D₅
unambiguous semidirect product	D₁₅⋊(C₇×D₅×C₁₇)

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₁₅⋊D₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₇×C₁₇

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

normal subgroups only

This group has 192 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) = 3570

3570 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 459);