#11789830

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Splittings

Sylow

C₃² ⋊ #1934

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂×AΓL(1,𝔽₉)
commutator	C₂×#157	C₂²×C₄
Fitting	C₂×C₃²×C₄	SD₁₆
socle	C₂²×C₃²	C₂×SD₁₆
prime radical	C₂²×GO⁺(4,𝔽₂)	C₂²
cosocle	C₂²×#157	C₂³
hypercenter	C₂×C₄	AΓL(1,𝔽₉)
hypocenter	C₃²	#1934
LCS	G ▷ C₂×#157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

358 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 96

Polycyclic presentation:

2^7,3^2|a^2=f,b^2=dfg,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=hi^2,i^a=h^2i^2,h^b=hi^2,i^b=h^2,h^c=h^2i,i^c=h,h^d=h^2i^2,i^d=h^2i,h^e=h^2i^2,i^e=h^2i,h^f=h^2,i^f=i^2,h^g=h^2,i^g=i^2

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 23841);