#44529181

order	31168
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₄₈₇ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₈₇
commutator, socle, prime radical	C₂²×C₄₈₇	C₂²×C₄
Fitting	C₄×Q₈×C₄₈₇	C₂
cosocle	C₂×C₄×C₄₈₇	C₂³
hypercenter	C₄×Q₈	D₄₈₇
hypocenter	C₄₈₇	#446
LCS	G ▷ C₂²×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

94 conjugacy classes of subgroups.

μ_t(G) = 31168

Polycyclic presentation:

2^6,487|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^486,g^c=g^486

4888 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31168, 680);