Finite Group Databasebeta

C2×#20295443 #28376131

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20295443

Splittings

SylowC109 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C8C22×D109
commutatorC2×C109C23×C8
FrattiniC8C23×D109
FittingC2×#131×C109C2
socleC22×C109C22×C8
prime radicalC2×#41×C109C4
cosocleC8×C109C24
hypercenterC2×#131D109
hypocenterC109C2×#504
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C8 ◁ C2×#131

368 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, 17609);