C₇×D₉×D₉₅ #37561019

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

Aliases

direct product	C₇×D₉×D₉₅
unambiguous semidirect product	(C₅×D₉)⋊(C₇×D₁₉)
unambiguous semidirect product	(D₉×C₁₉)⋊(C₇×D₅)

	subgroup	G/H
center, hypercenter	C₇	D₉×D₉₅
commutator, cosocle, hypocenter	C₅×C₉×C₁₉	C₂²×C₇
Frattini	C₃	D₃×C₇×D₉₅
Fitting	C₅×C₇×C₉×C₁₉	C₂²
socle	C₃×C₅×C₇×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₉
UCS	C₁ ◁ C₇

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

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

μ_t(G) = 5985

2058 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 151);