Finite Group Databasebeta

C2×C8×Dic214 #28345382

order13696
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×Dic214

Splittings

SylowC107 ⋊ C2×C8×Q8

Subgroups

subgroupG/H
centerC22×C8C2×D107
commutatorC2×C107C23×C8
FrattiniC2×C4C23×D107
FittingC2×C4×C8×C107C2
socle, prime radicalC23×C107C22×C4
cosocleC2×C4×C107C24
hypercenterC2×C4×C8D107
hypocenterC107C2×C8×Q8
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

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, 13431);