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#32977017

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

Aliases

No aliases for this group.

Splittings

C₇₃ ⋊ #8246

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1526	C₂
socle	C₂²×C₇₃	C₄×C₂²⋊C₄
prime radical	C₂³×C₇₃	#117
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1526	D₇₃
hypocenter	C₇₃	#8246
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1526

376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9344

Polycyclic presentation:

2^8,73|a^2=e,b^2=f,c^2=eh,d^2=g,e^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fgh,i^a=i^72,c^b=ch,d^b=dh,i^c=i^72

Conjugacy classes & character table

1432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 60601);