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C3×#72089 #11788473

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#72089

Splittings

SylowC32 ⋊ #1904

Subgroups

subgroupG/H
centerC2×C3#5220
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC2×C32×AGL(1,ℤ/8)C2
socleC2×C32#386
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#1904
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

841 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 22484);