Finite Group Databasebeta

#390×D109 #28365485

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct product#390×D109

Splittings

Fitting#390×C109 ⋊ C2
SylowC109 ⋊ C2×#390

Subgroups

subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#390×C109C2
socle, cosocleC23×C109C24
prime radicalC22×D4×D109C2
hypercenter#390D109
hypocenterC109C2×#390
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #390

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6963);