Finite Group Databasebeta

#261×D4⋊C8 #16780451

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#261×D4⋊C8

Splittings

FittingC13×D4⋊C8 ⋊ C4
SylowC13 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C2×C4×C8
FrattiniC42C22×#261
FittingC13×D4⋊C8C4
socleC22×C13C4×C22⋊C4
prime radicalC2×D4×D13C2×C4
cosocleC42×D13C23
hypercenterD4⋊C8#261
hypocenterC13C4×D4⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087100);