D₇×C₂₃×D₄₅ #44394398

order	28980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×C₂₃×D₄₅
unambiguous semidirect product	(C₅×D₇)⋊(D₉×C₂₃)
unambiguous semidirect product	(C₉×D₇)⋊(D₅×C₂₃)

	subgroup	G/H
center, hypercenter	C₂₃	D₇×D₄₅
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₂₃
Frattini	C₃	D₇×C₂₃×D₁₅
Fitting	C₅×C₇×C₉×C₂₃	C₂²
socle	C₃×C₅×C₇×C₂₃	C₂×D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₂₃

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

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

μ_t(G) = 7245

2760 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 67);