D₅×(C₂²⋊C₉)⋊C₂ #10623925

order	720
isoclinism	isoclinic class of D₅×(C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₅×(C₂²⋊C₉)⋊C₂
unambiguous semidirect product	(C₅×(C₂²⋊C₉)⋊C₂)⋊C₂
unambiguous semidirect product	(C₅⋊((C₂²⋊C₉)⋊C₂))⋊C₂
unambiguous semidirect product	(D₅×C₂²⋊C₉)⋊C₂

derived	C₅×C₂²⋊C₉ ⋊ C₂²
Sylow	C₅ ⋊ C₂×(C₂²⋊C₉)⋊C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₂²⋊C₉	C₂²
Frattini	C₃	D₅×S₄
Fitting, socle	C₂²×C₃×C₅	C₂×D₃
LCS	G ▷ C₅×C₂²⋊C₉
UCS	C₁

112 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.

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

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 90

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 394);