Finite Group Databasebeta

C2×C22⋊Q8×D107 #28349685

order13696
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×C22⋊Q8×D107

Splittings

FittingC2×C22⋊Q8×C107 ⋊ C2
SylowC107 ⋊ C22×C22⋊Q8

Subgroups

subgroupG/H
centerC23C23×D107
commutator, cosocleC22×C107C25
FrattiniC22C24×D107
FittingC2×C22⋊Q8×C107C2
socleC23×C107C24
prime radicalC24×D107C22
hypercenterC2×C22⋊Q8D107
hypocenterC107C22×C22⋊Q8
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 17734);