D₅×D₂₃×C₇⋊C₉ #44394367

order	28980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×D₂₃×C₇⋊C₉
unambiguous semidirect product	(D₅×C₂₃)⋊(C₂×C₇⋊C₉)
unambiguous semidirect product	(C₅×D₂₃)⋊(C₂×C₇⋊C₉)
unambiguous semidirect product	D₁₁₅⋊(C₂×C₇⋊C₉)
unambiguous semidirect product	(C₇×D₅×D₂₃)⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×ΓL(1,𝔽₈)×D₂₃
commutator, hypocenter	C₅×C₇×C₂₃	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅×C₇×C₂₃	C₂²×C₃
prime radical	C₃×C₇×D₅×D₂₃	C₃
LCS	G ▷ C₅×C₇×C₂₃
UCS	C₁ ◁ C₃

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

normal subgroups only

This group has 120 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) = 7245

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 36);