C₅×C₂₉×(C₃⋊D₃)⋊D₅ #39908167

order	26100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₂₉×(C₃⋊D₃)⋊D₅
unambiguous semidirect product	(C₃⋊D₃)⋊(C₅×D₅×C₂₉)
unambiguous semidirect product	D₁₅⋊(C₅×D₃×C₂₉)

	subgroup	G/H
center, hypercenter	C₅×C₂₉	(C₃⋊D₃)⋊D₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₂₉

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

normal subgroups only

This group has 224 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) = 870

3045 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 401);