(C₂×D₇)⋊(C₇⋊C₈) #13096048

order	1568
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

Aliases

(C₂×D₇)⋊(C₇⋊C₈)

C₇² ⋊ C₂²⋊C₈

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₇²
commutator	C₂×C₇²	C₂×C₈
Fitting, cosocle	C₂×C₄×C₇²	C₂²
socle	C₂²×C₇²	C₂×C₄
prime radical	C₂²×C₇×D₇	C₄
hypocenter	C₇²	C₂²⋊C₈
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂×C₄

133 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 133 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

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

μ_t(G) = 224

Polycyclic presentation:

2^5,7^2|b^2=c,c^2=e,b^a=bd,g^a=g^6,f^b=f^6

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1568, 214);