Finite Group Databasebeta

C2×#1057⋊C16 #16786590

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#1057⋊C16

Splittings

SylowC13 ⋊ C2×#1312

Subgroups

subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C2×C4×C16
FrattiniC2×C8C22×#261
FittingC22×C13×C16C4
socle, prime radicalC23×C13C4×C8
cosocleC8×Dic13C23
hypercenterC22×C16#261
hypocenterC13C2×#1312
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C22×C16

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1093239);