Finite Group Databasebeta

C2×C22⋊C8×D107 #28344891

order13696
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D107

Splittings

FittingC2×C22⋊C8×C107 ⋊ C2
SylowC107 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D107
commutatorC2×C107C23×C8
FrattiniC2×C4C23×D107
FittingC2×C22⋊C8×C107C2
socleC23×C107C22×C4
prime radicalC24×D107C4
cosocleC2×C4×C107C24
hypercenterC2×C22⋊C8D107
hypocenterC107C22×C22⋊C8
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 12940);