#24910770

order	10624
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₈₃ ⋊ #2402

	subgroup	G/H
center	C₂²×C₄	C₂²×D₈₃
commutator, socle, prime radical, cosocle	C₂³×C₈₃	C₂⁴
Frattini	C₂³	C₂³×D₈₃
Fitting	C₄×C₄⋊C₄×C₈₃	C₂
hypercenter	C₄×C₄⋊C₄	D₈₃
hypocenter	C₈₃	#2402
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

400 conjugacy classes of subgroups.

Polycyclic presentation:

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

1684 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 7817);