C₂×D₃×C₁₁²×ΓL(1,𝔽₈) #44479165

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₁² · Schur multiplier (H₂) = C₂×C₁₁

Aliases

direct product	C₂×D₃×C₁₁²×ΓL(1,𝔽₈)
unambiguous semidirect product	C₃⋊(C₂²×C₁₁²×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₁₁²×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×D₃×C₇)⋊(C₃×C₁₁²)
unambiguous semidirect product	(C₂×D₃×C₇×C₁₁)⋊(C₃×C₁₁)

	subgroup	G/H
center, hypercenter	C₂×C₁₁²	D₃×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃×C₁₁²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₁²	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₁₁²

616 conjugacy classes of subgroups; only the 294 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 294 normal subgroups are shown.

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

μ_t(G) = 5082

3630 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 388);