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#15688969

order	3008
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄²

Aliases

No aliases for this group.

Splittings

C₄₇ ⋊ #376

Subgroups

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄²
Frattini	C₂³	C₂²×D₄₇
Fitting	C₂×C₄²×C₄₇	C₂
socle, prime radical, cosocle	C₂³×C₄₇	C₂³
hypercenter	C₂×C₄²	D₄₇
hypocenter	C₄₇	#376
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3008

Polycyclic presentation:

2^6,47|a^2=e,b^2=f,c^2=d,b^a=bd,g^b=g^46

Conjugacy classes & character table

776 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 395);