Finite Group Databasebeta

C2×#13112792 #15772619

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13112792

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8D52
commutatorC4×C13C22×C16
FrattiniC4×C8C22×D13
FittingC2×C4×C13×C16C2
socleC23×C13C22⋊C8
prime radicalC22×D52C8
cosocleC4×C8×C13C23
hypercenterC2×C4×C16D13
hypocenterC13C2×D4⋊C16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 79268);