Finite Group Databasebeta

C2×#20292555 #28339688

order13696
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20292555

Splittings

SylowC107 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D107
commutator, cosocleC23×C107C24
FrattiniC23C23×D107
FittingC22×C22⋊C4×C107C2
socleC24×C107C23
prime radicalC25×C107C22
hypercenterC22×C22⋊C4D107
hypocenterC107C2×#397
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

Conjugacy classes & character table

2164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 7737);