Finite Group Databasebeta

C2×#20292623 #28344957

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

Aliases

direct productC2×#20292623

Splittings

SylowC107 ⋊ C2×#416

Subgroups

subgroupG/H
centerC22×C4C22⋊D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
Fitting, prime radicalC22×#41×C107C2
socleC23×C107C2×D4
cosocleC2×C4×C107C24
hypercenterC22×#41D107
hypocenterC107C2×#416
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

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, 13006);