C₅²×ΓL(1,𝔽₈)×D₂₁ #36348024

order	22050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×ΓL(1,𝔽₈)×D₂₁
unambiguous semidirect product	C₃⋊(C₅²×D₇×ΓL(1,𝔽₈))

	subgroup	G/H
center, hypercenter	C₅²	ΓL(1,𝔽₈)×D₂₁
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₅²

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

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

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

μ_t(G) = 3150

1500 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 461);