Finite Group Databasebeta

C8×#88116 #16780525

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#88116

Splittings

FittingC8×D4×C13 ⋊ C4
SylowC13 ⋊ C8×#104

Subgroups

subgroupG/H
centerC2×C8C22⋊#261
commutatorC4×C13C2×C4×C8
FrattiniC42C22×#261
FittingC8×D4×C13C4
socleC22×C13C4×C22⋊C4
prime radicalC2×#6129C2×C4
cosocleC42×D13C23
hypercenterC8×D4#261
hypocenterC13C8×#104
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D4

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087174);