C₅×C₁₃×D₇×D₁₅ #41031973

order	27300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₁₃×D₇×D₁₅
unambiguous semidirect product	(C₃×D₇)⋊(C₅×D₅×C₁₃)
unambiguous semidirect product	(C₅×D₇)⋊(C₅×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₇×D₁₅
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₃	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₅×C₁₃

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 2730

2925 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 863);