Finite Group Databasebeta

#261×C22⋊C16 #16789288

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct product#261×C22⋊C16

Splittings

FittingC13×C22⋊C16 ⋊ C4
SylowC13 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#261
commutatorC2×C13C2×C4×C16
FittingC13×C22⋊C16C4
socleC22×C13C2×C4×C8
prime radicalC23×D13C2×C8
cosocleC2×C8×D13C23
hypercenterC22⋊C16#261
hypocenterC13C4×C22⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22⋊C16

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095937);