C₂×C₃×C₃⋊(C₇⋊(C₁₁⋊D₁₁)) #44479267

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

Aliases

direct product	C₂×C₃×C₃⋊(C₇⋊(C₁₁⋊D₁₁))
unambiguous semidirect product	(C₂×C₃)⋊(C₃×C₇⋊(C₁₁⋊D₁₁))
unambiguous semidirect product	(C₂×C₁₁)⋊(C₃×D₂₃₁)

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(C₇⋊(C₁₁⋊D₁₁))
commutator, cosocle, hypocenter	C₃×C₇×C₁₁²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₁²	C₂
LCS	G ▷ C₃×C₇×C₁₁²
UCS	C₁ ◁ C₂×C₃

616 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

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

μ_t(G) = 10164

7632 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 490);