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H(3,𝔽₃)×C₃₇₉⋊C₃ #44501948

order	30699
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₃₇₉⋊C₃

Splittings

Fitting	H(3,𝔽₃)×C₃₇₉ ⋊ C₃
Sylow	C₃₇₉ ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃²×C₃₇₉⋊C₃
commutator, socle, cosocle	C₃×C₃₇₉	C₃³
Fitting	H(3,𝔽₃)×C₃₇₉	C₃
hypercenter	H(3,𝔽₃)	C₃₇₉⋊C₃
hypocenter	C₃₇₉	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3411

Conjugacy classes & character table

1419 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30699, 40);