Finite Group Databasebeta

C22×D13⋊M32 #16809613

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×D13⋊M32
unambiguous semidirect productD13⋊(C22×M32)

Splittings

SylowC13 ⋊ C23×M32

Subgroups

subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C24×C8
FrattiniC4C24×#261
FittingC23×C8×C13C4
socleC23×C13C22×C8
prime radicalC24×D13C8
cosocle#1055C25
hypercenterC23×C8#261
hypocenterC13C23×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C23×C8

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1116262);