C₁₉×D₂₁⋊D₁₅ #37561570

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

Aliases

direct product	C₁₉×D₂₁⋊D₁₅
unambiguous semidirect product	D₂₁⋊(C₁₉×D₁₅)

	subgroup	G/H
center, hypercenter	C₁₉	D₂₁⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₁₉

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 3990

1881 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 702);