Finite Group Databasebeta

C2×#103×D107 #28344949

order13696
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#103×D107

Splittings

FittingC2×#103×C107 ⋊ C2
SylowC107 ⋊ C22×#103

Subgroups

subgroupG/H
centerC23D4×D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
FittingC2×#103×C107C2
socleC23×C107C2×D4
prime radicalC23×D107D4
cosocleC2×C4×C107C24
hypercenterC2×#103D107
hypocenterC107C22×#103
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 12998);