C₇×D₅×C₃⋊D₃×C₁₉ #37561604

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₇×D₅×C₃⋊D₃×C₁₉
unambiguous semidirect product	(C₃×D₅)⋊(D₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₅×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₁₉

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

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

μ_t(G) = 5985

3192 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 736);