#33113402

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	C₂×#14556559
commutator, prime radical, cosocle	C₂⁴×C₇₃	C₂⁴
Frattini	C₂⁴	C₂³×D₇₃
Fitting	C₇₃×#2310	C₂
socle	C₂²×C₇₃	C₂×#120
hypercenter	#2310	D₇₃
hypocenter	C₇₃	#23470
LCS	G ▷ C₂⁴×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2310

1178 conjugacy classes of subgroups.

μ_t(G) = 4672

Polycyclic presentation:

2^8,73|a^2=e,b^2=e,c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^b=i^72,d^c=dh

1630 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 196986);