Finite Group Databasebeta

#123×Dic109 #28365555

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#123×Dic109

Splittings

SylowC109 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
FittingC2×#123×C109C2
socle, cosocleC23×C109C24
prime radicalC22×D4×C109C22
hypercenterC2×#123D109
hypocenterC109C4×#123
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×#123

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

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, 7033);