Finite Group Databasebeta

← Prev (#11919209) Next (#11919211) →

C2×C3×D3×H(5,𝔽2) #11919210

order1152
automorphism?
homologyAbelianization (H1) = C26×C3 · Schur multiplier (H2) = C214

Aliases

direct productC2×C3×D3×H(5,𝔽2)

Splittings

FittingC2×C32×H(5,𝔽2) ⋊ C2
SylowC32 ⋊ C22×H(5,𝔽2)

Subgroups

subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC2×C3C26×C3
FrattiniC2C25×C3×D3
FittingC2×C32×H(5,𝔽2)C2
socleC22×C32C25
hypercenterC2×C3×H(5,𝔽2)D3
hypocenterC3C22×C3×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×H(5,𝔽2)

13569 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D32×H(5,𝔽2), C2×C3×D3×B(4,𝔽2), C2×C3×D3×#453, …
maximal normal subgroup ofC2×D32×H(5,𝔽2), C2×C3×D3×B(4,𝔽2), C2×C3×D3×#453, …
maximal quotient ofD3×H(5,𝔽2)×AGL(1,𝔽7), C2×H(5,𝔽2)×AGL(1,ℤ/9), C3×D3×#3484, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153221);