#26134802

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂²×C₈
Fitting	C₂×C₈×Q₈×C₄₇	C₂
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×C₈×Q₈	D₄₇
hypocenter	C₄₇	#13264
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₈×Q₈

386 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,47|a^2=f,b^2=def,c^2=e,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^46,c^b=ch,i^b=i^46

1928 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 88092);