#34013862

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Splittings

Fitting	#362×C₇₃ ⋊ C₄
Sylow	C₇₃ ⋊ #13157

Subgroups

	subgroup	G/H
center	C₂	#22626023
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×#64408
Fitting	#362×C₇₃	C₄
socle	C₂×C₇₃	#1936
prime radical	C₂²×D₇₃	#137
cosocle	C₂×C₈×D₇₃	C₂³
hypercenter	#362	#64408
hypocenter	C₇₃	#13157
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #362

296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4672

Polycyclic presentation:

2^8,73|a^2=f,b^2=dfg,c^2=d,d^2=g,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,i^a=i^46,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^27,e^c=eh,f^c=fh,i^f=i^72

Conjugacy classes & character table

322 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1097446);