Finite Group Databasebeta

#117×C22⋊D13 #16022319

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct product#117×C22⋊D13

Splittings

FittingC22×C13×#117 ⋊ C2
SylowC13 ⋊ D4×#117

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C13×#117C2
socle, cosocleC23×C13C25
prime radicalC23×C22⋊D13C22
hypercenterC22×#117D13
hypocenterC13D4×#117
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#117

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328968);