C₅²×D₇×D₃₉ #41031966

order	27300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×D₇×D₃₉
unambiguous semidirect product	(C₃×D₇)⋊(C₅²×D₁₃)
unambiguous semidirect product	(C₁₃×D₇)⋊(C₅²×D₃)

	subgroup	G/H
center, hypercenter	C₅²	D₇×D₃₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₃	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₅²

320 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

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

μ_t(G) = 6825

2625 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 856);