Finite Group Databasebeta

#117×Dic109 #28365375

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic109

Splittings

SylowC109 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C22×C42
FrattiniC23C23×D109
FittingC2×#117×C109C2
socle, cosocleC23×C109C24
prime radicalC24×C109C23
hypercenterC2×#117D109
hypocenterC109C4×#117
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×#117

752 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, 6853);