Finite Group Databasebeta

C2×#20294906 #28365451

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20294906

Splittings

SylowC109 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
Fitting, prime radicalC23×D4×C109C2
socleC24×C109C23
cosocleC23×C109C24
hypercenterC23×D4D109
hypocenterC109C2×#386
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×D4

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6929);