Finite Group Databasebeta

#117×#1057 #16797268

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×#1057

Splittings

SylowC13 ⋊ C8×#117

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC2×C13×#117C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC2×#117#261
hypocenterC13C8×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#117

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1103917);