Finite Group Databasebeta

C8×#6397 #13244355

order1792
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#6397

Splittings

FittingC7×C8×M16 ⋊ C2
SylowC7 ⋊ C8×#100

Subgroups

subgroupG/H
centerC2×C8(C2×D7)⋊C4
commutatorC22×C7C2×C4×C8
FrattiniC2×C42C22×D7
FittingC7×C8×M16C2
socleC22×C7C4×C22⋊C4
prime radicalC22×D28C2×C4
cosocleC2×C42×C7C23
hypercenterC8×M16D7
hypocenterC7C8×#100
LCSG ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×M16

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 60127);