Finite Group Databasebeta

C2×C4×M16×D67 #31719215

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×M16×D67

Splittings

FittingC2×C4×M16×C67 ⋊ C2
SylowC67 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC2×C42C22×D67
commutatorC2×C67C23×C42
FrattiniC2×C4C24×D67
FittingC2×C4×M16×C67C2
socleC23×C67C23×C4
prime radicalC24×D67C2×C4
cosocleC2×C4×C67C25
hypercenterC2×C4×M16D67
hypocenterC67C22×C4×M16
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1032952);