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C2×D32×M16 #11918442

order1152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×D32×M16

Splittings

FittingC2×C32×M16 ⋊ C22
SylowC32 ⋊ C23×M16

Subgroups

subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C23×C4
prime radicalC23×D32C4
cosocleC32×C4C25
hypercenterC2×M16D32
hypocenterC32C23×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

3589 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D32×AGL(1,ℤ/8), C2×D3×M16×C3⋊D3, C4×D32×M16, …
maximal normal subgroup ofC2×D32×AGL(1,ℤ/8), C4×D32×M16, C2×D32×#104, …
maximal quotient ofC2×D32×#97, C2×D3×M16×C3⋊D3, C4×D32×M16

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 152453);