Finite Group Databasebeta

#427×D109 #28371608

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#427×D109

Splittings

Fitting#427×C109 ⋊ C2
SylowC109 ⋊ C2×#427

Subgroups

subgroupG/H
centerC2×C4D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#427×C109C2
socleC22×C109C22×D4
prime radicalC23×D109D4
cosocleC2×C4×C109C24
hypercenter#427D109
hypocenterC109C2×#427
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

512 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, 13086);