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C₃×#13133548 #19103160

order	5103
automorphism	?
homology	Abelianization (H₁) = C₃⁴ · Schur multiplier (H₂) = C₃⁶

Aliases

C₃×#13133548

Splittings

C₇ ⋊ C₃×C₉⋊H(3,𝔽₃)

Subgroups

	subgroup	G/H
center	C₃³	C₃²×ΓL(1,𝔽₈)
commutator	C₃²×C₇	C₃⁴
Frattini	C₃²	C₃³×ΓL(1,𝔽₈)
Fitting	C₃²×C₇×H(3,𝔽₃)	C₃
socle	C₃³×C₇	C₃³
hypercenter	C₃²×H(3,𝔽₃)	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×C₉⋊H(3,𝔽₃)
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

1328 conjugacy classes of subgroups; only the 346 normal subgroups are shown.

normal subgroups only

This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 346 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

351 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5103, 3311);