Finite Group Databasebeta

C2×#117×D109 #28376194

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#117×D109

Splittings

FittingC2×#117×C109 ⋊ C2
SylowC109 ⋊ C22×#117

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC2×#117×C109C2
socleC23×C109C24
prime radicalC24×D109C22
cosocleC22×C109C25
hypercenterC2×#117D109
hypocenterC109C22×#117
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×#117

1880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

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, 17672);