C₅²×D₃×C₁₃×D₇ #41031965

order	27300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₁₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×D₃×C₁₃×D₇
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₅²×C₁₃)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₅²×C₁₃)
unambiguous semidirect product	D₂₁⋊(C₂×C₅²×C₁₃)

	subgroup	G/H
center, hypercenter	C₅²×C₁₃	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₃	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅²×C₁₃

320 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

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

μ_t(G) = 6825

4875 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 855);