C₇×C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇))) #36348044

order	22050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₇×C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))
unambiguous semidirect product	C₃⋊(C₇×C₅⋊(C₅⋊AGL(1,𝔽₇)))
unambiguous semidirect product	C₅⋊(C₇×C₃⋊(C₅⋊AGL(1,𝔽₇)))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₇×C₃⋊(C₅⋊D₅))

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))
commutator, cosocle, hypocenter	C₃×C₅²×C₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₇

304 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

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

μ_t(G) = 3150

1344 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 481);