Finite Group Databasebeta

#322×D109 #28361306

order13952
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#322×D109

Splittings

Fitting#322×C109 ⋊ C2
SylowC109 ⋊ C2×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×D109
commutatorC2×C109C2×C4×C8
Fitting#322×C109C2
socleC22×C109C2×C42
prime radicalC22×D109C42
cosocleC42×C109C23
hypercenter#322D109
hypocenterC109C2×#322
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C42 ◁ #322

248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2784);