#44500524

order	30656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₄₇₉ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₇₉
commutator, socle, prime radical	C₂²×C₄₇₉	C₂²×C₄
Fitting	C₄⋊C₈×C₄₇₉	C₂
cosocle	C₂×C₄×C₄₇₉	C₂³
hypercenter	C₄⋊C₈	D₄₇₉
hypocenter	C₄₇₉	#446
LCS	G ▷ C₂²×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

94 conjugacy classes of subgroups.

μ_t(G) = 30656

Polycyclic presentation:

2^6,479|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^478,g^c=g^478

4808 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 678);