Finite Group Databasebeta

C2×#20293244 #28349835

order13696
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20293244

Splittings

SylowC107 ⋊ C2×#542

Subgroups

subgroupG/H
centerC23C23×D107
commutator, cosocleC22×C107C25
FrattiniC22C24×D107
Fitting, prime radicalC2×#121×C107C2
socleC23×C107C24
hypercenterC2×#121D107
hypocenterC107C2×#542
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#121

1132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

Conjugacy classes & character table

1528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 17884);