#24907616

order	10624
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₈₃ ⋊ #1843

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₈₃
commutator, socle, prime radical	C₂³×C₈₃	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₈₃	C₂
cosocle	C₂²×C₄×C₈₃	C₂³
hypercenter	C₂×C₄⋊C₈	D₈₃
hypocenter	C₈₃	#1843
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Polycyclic presentation:

2^7,83|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=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, 4663);