Finite Group Databasebeta

M16×#1136 #13319506

order1792
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productM16×#1136

Splittings

SylowC7 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC42C23×D7
commutator, socleC22×C7C22×C42
FittingC2×C4×C7×M16C2
prime radicalC24×C7C42
cosocleC42×C7C24
hypercenterC2×C4×M16D7
hypocenterC7M162
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C42 ◁ C2×C4×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 135278);