Finite Group Databasebeta

C2×#20292522 #28338909

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

Aliases

direct productC2×#20292522

Splittings

SylowC107 ⋊ C2×#389

Subgroups

subgroupG/H
centerC24C22×D107
commutatorC22×C107C23×C4
FrattiniC23C23×D107
FittingC22×C4⋊C4×C107C2
socle, prime radicalC24×C107C23
cosocleC23×C107C24
hypercenterC22×C4⋊C4D107
hypocenterC107C2×#389
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C24 ◁ C22×C4⋊C4

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

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, 6958);