Finite Group Databasebeta

C2×#20293134 #28349699

order13696
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20293134

Splittings

FittingC22×#41×C107 ⋊ C2
SylowC107 ⋊ C2×#525

Subgroups

subgroupG/H
centerC22×C4C22×D107
commutator, cosocleC22×C107C25
FrattiniC22C24×D107
FittingC22×#41×C107C2
socleC23×C107C24
hypercenterC22×#41D107
hypocenterC107C2×#525
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C22×#41

1880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

Conjugacy classes & character table

2176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 17748);