C₂×C₁₃×C₃⋊D₁₉₅ #44478352

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₁₃×C₃⋊D₁₉₅
unambiguous semidirect product	(C₂×C₃)⋊(C₁₃×D₁₉₅)
unambiguous semidirect product	(C₂×C₅)⋊(C₁₃×C₃⋊D₃₉)
unambiguous semidirect product	(C₂×C₁₃)⋊(C₁₃×C₃⋊D₁₅)

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₁₉₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₃²	C₂
LCS	G ▷ C₃²×C₅×C₁₃
UCS	C₁ ◁ C₂×C₁₃

384 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

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

μ_t(G) = 2340

7644 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 941);