C₂×C₅×C₁₃×D₁₁₇ #44477790

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×C₁₃×D₁₁₇
unambiguous semidirect product	(C₂×C₉)⋊(C₅×C₁₃×D₁₃)
unambiguous semidirect product	(C₂×C₁₃)⋊(C₅×C₁₃×D₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²×C₅×C₁₃
Frattini	C₃	C₂×C₅×C₁₃×D₃₉
Fitting	C₂×C₅×C₉×C₁₃²	C₂
socle	C₂×C₃×C₅×C₁₃²	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂×C₅×C₁₃

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

normal subgroups only

This group has 192 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) = 2340

7800 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 379);