Finite Group Databasebeta

C2×#20292369 #28335045

order13696
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20292369

Splittings

SylowC107 ⋊ C2×#330

Subgroups

subgroupG/H
centerC23C22⋊Dic107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
FittingC2×#125×C107C2
socle, prime radicalC23×C107C22⋊C4
cosocleC42×C107C23
hypercenterC2×#125D107
hypocenterC107C2×#330
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

Conjugacy classes & character table

1522 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 3094);