C₅²×C₃⋊(ΓL(1,𝔽₈)⋊D₇) #36348023

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

Aliases

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

	subgroup	G/H
center, hypercenter	C₅²	C₃⋊(ΓL(1,𝔽₈)⋊D₇)
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

352 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

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

μ_t(G) = 1575

1425 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 460);