C₄×#87718 #13098205

order	1600
isoclinism	isoclinic class of Dic₅₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂₅ ⋊ C₄×C₄⋊C₄

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₅
commutator	C₂×C₂₅	C₂×C₄²
Frattini, socle, prime radical	C₂³×C₅	C₂²×D₅
Fitting	C₂×C₄²×C₂₅	C₂
cosocle	C₂³×C₂₅	C₂³
hypercenter	C₂×C₄²	D₂₅
hypocenter	C₂₅	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

291 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 291 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

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

μ_t(G) = 1600

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 557);