C₇×C₃⋊(ΓL(1,𝔽₈)⋊D₂₅) #36347753

order	22050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₃⋊(ΓL(1,𝔽₈)⋊D₂₅)
unambiguous semidirect product	C₃⋊(C₇×ΓL(1,𝔽₈)⋊D₂₅)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₇×D₇₅)
unambiguous semidirect product	C₂₅⋊(C₇×C₃⋊AGL(1,𝔽₇))
unambiguous semidirect product	D₅₂₅⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₂₅)
commutator, cosocle, hypocenter	C₃×C₇×C₂₅	C₂×C₃×C₇
Frattini	C₅	C₇×C₃⋊(C₅⋊AGL(1,𝔽₇))
Fitting	C₃×C₇²×C₂₅	C₂×C₃
socle	C₃×C₅×C₇²	C₃×D₅
LCS	G ▷ C₃×C₇×C₂₅
UCS	C₁ ◁ C₇

114 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 40 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, 190);