Finite Group Databasebeta

#102×#1057 #16780574

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

Aliases

direct product#102×#1057

Splittings

SylowC13 ⋊ C8×#102

Subgroups

subgroupG/H
centerC23D4×#261
commutatorC4×C13C2×C4×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#102C4
socleC23×C13C4×D4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×#102#261
hypocenterC13C8×#102
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1087223);