Finite Group Databasebeta

M16×C7⋊C16 #13262808

order1792
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×C7⋊C16

Splittings

SylowC7 ⋊ C16×M16

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D7
commutatorC2×C7C2×C4×C16
FittingC7×C8×M16C2
socleC22×C7C2×C4×C8
prime radicalC23×C7C4×C8
cosocleC4×C7×C8C23
hypercenterC8×M16D7
hypocenterC7C16×M16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C8 ◁ C8×M16

306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

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, 78580);