ΓL(1,𝔽₈)×D₁₅⋊D₁₇ #36339396

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	ΓL(1,𝔽₈)×D₁₅⋊D₁₇
unambiguous semidirect product	D₁₅⋊(ΓL(1,𝔽₈)×D₁₇)
unambiguous semidirect product	D₅₁⋊(D₅×ΓL(1,𝔽₈))
unambiguous semidirect product	D₈₅⋊(D₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₇×D₁₅⋊D₁₇)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₁₇	C₂²×C₃
LCS	G ▷ C₃×C₅×C₇×C₁₇
UCS	C₁

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

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

μ_t(G) = 1785

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 228);