Finite Group Databasebeta

C2×#20292611 #28344936

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

Aliases

direct productC2×#20292611

Splittings

SylowC107 ⋊ C2×#413

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic107
commutatorC22×C107C23×C4
FrattiniC2×C4C23×D107
Fitting, prime radicalC22×#41×C107C2
socleC22×C107C2×C22⋊C4
cosocleC2×C4×C107C24
hypercenterC22×#41D107
hypocenterC107C2×#413
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

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, 12985);