Finite Group Databasebeta

#108×Dic26 #15881811

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct product#108×Dic26

Splittings

SylowC13 ⋊ Q8×#108

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#108C2
socleC22×C13C22×C4⋊C4
prime radicalC23×C13C22×Q8
cosocleC22×C4×C13C24
hypercenterC4×#108D13
hypocenterC13Q8×#108
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 188460);