Finite Group Databasebeta

C2×#20292560 #28339694

order13696
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20292560

Splittings

SylowC107 ⋊ C2×#398

Subgroups

subgroupG/H
centerC24C22×D107
commutator, cosocleC23×C107C24
FrattiniC23C23×D107
FittingC22×C4⋊C4×C107C2
socle, prime radicalC24×C107C23
hypercenterC22×C4⋊C4D107
hypocenterC107C2×#398
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C24 ◁ C22×C4⋊C4

692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

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, 7743);