#11764427

order	1120
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₅×D₇
commutator	C₂×C₅×C₇	C₂×C₈
Fitting, cosocle	C₂×C₄×C₅×C₇	C₂²
socle	C₂²×C₅×C₇	C₂×C₄
prime radical	C₂²×D₃₅	C₄
hypocenter	C₅×C₇	C₂²⋊C₈
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₄

100 conjugacy classes of subgroups.

μ_t(G) = 560

Polycyclic presentation:

2^5,5,7|a^2=d,b^2=cde,d^2=e,b^a=bc,g^a=g^6,f^b=f^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 33);