Finite Group Databasebeta

#117×#89137 #28379465

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

Aliases

direct product#117×#89137

Splittings

Fitting#117×C109 ⋊ C4
SylowC109 ⋊ C4×#117

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C22×C42
FrattiniC22C23×#89137
Fitting#117×C109C4
socleC22×C109C23×C4
prime radicalC23×D109C23
cosocleC22×D109C24
hypercenter#117#89137
hypocenterC109C4×#117
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ #117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20943);