Finite Group Databasebeta

C2×#22554489 #30682717

order16832
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22554489

Splittings

FittingC2×D8×C263 ⋊ C2
SylowC263 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D263
commutator, cosocleC4×C263C24
FrattiniC4C23×D263
FittingC2×D8×C263C2
socleC22×C263C2×D4
hypercenterC2×D8D263
hypocenterC263C2×#135
LCSG ▷ C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

1862 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 1328);