#24910757

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

Aliases

No aliases for this group.

C₈₃ ⋊ #2399

	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	#2399
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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=e,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^82,c^b=cg

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 7804);