D₇×#859 #13057075

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

derived	C₇×SL(2,𝔽₃) ⋊ C₂×C₄
Sylow	C₇ ⋊ C₂×#859

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₇×S₄
commutator, hypocenter	C₇×SL(2,𝔽₃)	C₂×C₄
Fitting	C₂×C₇×Q₈	C₂×D₃
socle	C₂²×C₇	C₂×S₄
prime radical	C₂×D₇×SL(2,𝔽₃)	C₂
cosocle	C₂×C₇×SL(2,𝔽₃)	C₂²
LCS	G ▷ C₇×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

194 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 224

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 6364);