#30746262

order	17152
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

C₆₇ ⋊ #8134

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₆₇
commutator, socle, prime radical	C₂³×C₆₇	C₂×C₄²
Fitting	C₆₇×#1273	C₂
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#1273	D₆₇
hypocenter	C₆₇	#8134
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄² ◁ #1273

414 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 17152

Polycyclic presentation:

2^8,67|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=ch,c^b=cg,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, 59999);