#32977140

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₇₃ ⋊ #8265

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₇₃
commutator, socle, prime radical	C₂³×C₇₃	C₂×C₄²
Fitting	C₄×C₄⋊C₈×C₇₃	C₂
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	C₄×C₄⋊C₈	D₇₃
hypocenter	C₇₃	#8265
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₄⋊C₈

438 conjugacy classes of subgroups.

μ_t(G) = 18688

Polycyclic presentation:

2^8,73|a^2=e,b^2=f,c^2=de,e^2=g,f^2=h,b^a=bd,c^a=ch,i^a=i^72,c^b=cg,i^b=i^72,i^c=i^72

2968 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 60724);