C₃²×D₃₅⋊D₁₇ #36339451

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃²×D₃₅⋊D₁₇
unambiguous semidirect product	D₈₅⋊(C₃²×D₇)

	subgroup	G/H
center, hypercenter	C₃²	D₃₅⋊D₁₇
commutator, cosocle, hypocenter	C₅×C₇×C₁₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂²
LCS	G ▷ C₅×C₇×C₁₇
UCS	C₁ ◁ C₃²

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

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

μ_t(G) = 5355

1548 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 283);