#24909371

order	10624
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₈₃ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₈₃
commutator, socle, prime radical	C₂²×C₈₃	C₂²×C₈
Fitting	C₄×C₁₆×C₈₃	C₂
cosocle	C₂×C₈×C₈₃	C₂³
hypercenter	C₄×C₁₆	D₈₃
hypocenter	C₈₃	#2183
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

126 conjugacy classes of subgroups.

Polycyclic presentation:

2^7,83|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^82

2680 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 6418);