Q₈×#6016 #13098775

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

C₂₅ ⋊ C₈×Q₈

	subgroup	G/H
center	C₂²	C₂²×#1035
commutator	C₂×C₂₅	C₂²×C₈
Frattini, socle, prime radical	C₂²×C₅	C₂²×AGL(1,𝔽₅)
Fitting	C₂×Q₈×C₂₅	C₄
cosocle	C₂×Dic₂₅	C₂³
hypercenter	C₂×Q₈	#1035
hypocenter	C₂₅	C₈×Q₈
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

153 conjugacy classes of subgroups.

μ_t(G) = 1600

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 1127);