#13098250

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₅ ⋊ #389

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator	C₂²×C₂₅	C₂²×C₄
Frattini, socle, prime radical	C₂³×C₅	C₂²×D₅
Fitting	C₂×C₄⋊C₄×C₂₅	C₂
cosocle	C₂³×C₂₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₂₅
hypocenter	C₂₅	#389
LCS	G ▷ C₂²×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

255 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

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

μ_t(G) = 1600

Polycyclic presentation:

2^6,5^2|a^2=f,b^2=e,c^2=d,g^5=h,b^a=bf,g^a=g^4h^4,h^a=h^4,c^b=ce

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 602);