#34088018

order	19648
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₃₀₇ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₀₇
commutator, socle, prime radical	C₂²×C₃₀₇	C₂²×C₄
Fitting	C₄×Q₈×C₃₀₇	C₂
cosocle	C₂×C₄×C₃₀₇	C₂³
hypercenter	C₄×Q₈	D₃₀₇
hypocenter	C₃₀₇	#446
LCS	G ▷ C₂²×C₃₀₇ ▷ C₃₀₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

94 conjugacy classes of subgroups.

μ_t(G) = 19648

Polycyclic presentation:

2^6,307|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^306,g^c=g^306

3088 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19648, 680);