Finite Group Databasebeta

C8×D7×M16 #13319366

order1792
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×D7×M16

Splittings

FittingC7×C8×M16 ⋊ C2
SylowC7 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC4×C8C22×D7
commutatorC2×C7C22×C4×C8
FrattiniC42C23×D7
FittingC7×C8×M16C2
socleC22×C7C22×C42
prime radicalC23×D7C42
cosocleC42×C7C24
hypercenterC8×M16D7
hypocenterC7C2×C8×M16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C8 ◁ C8×M16

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 135138);