Finite Group Databasebeta

C2×C4×(C2×D107)⋊C4 #28338792

order13696
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D107)⋊C4

Splittings

FittingC22×C42×C107 ⋊ C2
SylowC107 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D107
commutatorC2×C107C22×C42
FrattiniC23C23×D107
FittingC22×C42×C107C2
socleC24×C107C23
prime radicalC24×D107C22
cosocleC23×C107C24
hypercenterC22×C42D107
hypocenterC107C2×C4×C22⋊C4
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 6841);