Finite Group Databasebeta

#108×#1055 #15754213

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

Aliases

direct product#108×#1055

Splittings

SylowC13 ⋊ C8×#108

Subgroups

subgroupG/H
centerC42D4×D13
commutatorC4×C13C2×C4×C8
FrattiniC2×C42C22×D13
FittingC4×C13×#108C2
socleC22×C13C4×C4⋊C4
prime radicalC23×C13C4×Q8
cosocleC2×C42×C13C23
hypercenterC4×#108D13
hypocenterC13C8×#108
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#108

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 60862);