#10593207

order	576
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₂×C₄
Fitting	C₂×C₃×Q₈	C₂×D₃
socle	C₂²×C₃	C₂×S₄
prime radical	C₂×C₃⋊GL(2,𝔽₃)	C₂
cosocle	C₂×C₃×SL(2,𝔽₃)	C₂²
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

175 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 175 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 96

Polycyclic presentation:

2^3,3^2,2^3|a^2=ch,b^2=c,f^2=h,g^2=h,b^a=bh,e^a=e^2,d^b=d^2,f^b=gh,g^b=fh,f^d=g,g^d=fgh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 5089);