C₂×C₇×C₃⋊D₃₅₇ #44473023

order	29988
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₇×C₃⋊D₃₅₇
unambiguous semidirect product	(C₂×C₃)⋊(C₇×D₃₅₇)
unambiguous semidirect product	(C₂×C₇)⋊(C₇×C₃⋊D₅₁)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₇×C₃⋊D₂₁)

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊D₃₅₇
commutator, cosocle, hypocenter	C₃²×C₇×C₁₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₃²×C₇×C₁₇
UCS	C₁ ◁ C₂×C₇

312 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

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

μ_t(G) = 4284

7518 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 664);