Finite Group Databasebeta

#135×#1057 #16795184

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct product#135×#1057

Splittings

SylowC13 ⋊ C8×#135

Subgroups

subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
Fitting, prime radicalC2×C13×#135C4
socleC22×C13C2×C4×D4
cosocleC4×Dic13C24
hypercenterC2×#135#261
hypocenterC13C8×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

750 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, 1101833);