#30864172

order	17152
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²×C₈	C₂²×D₆₇
commutator, socle, prime radical	C₂³×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₈×C₄⋊C₄×C₆₇	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₆₇
hypocenter	C₆₇	#21676
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₈×C₄⋊C₄

658 conjugacy classes of subgroups.

μ_t(G) = 17152

Polycyclic presentation:

2^8,67|a^2=g,b^2=f,c^2=e,d^2=eg,g^2=h,b^a=be,c^a=cf,c^b=ch,i^b=i^66,i^c=i^66

2728 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 177909);