Finite Group Databasebeta

C2×#20299487 #28406776

order14464
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20299487

Splittings

SylowC113 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C4C2×#90673
commutatorC2×C113C2×C4×C8
FrattiniC2×C4C22×#90673
FittingC22×C8×C113C4
socle, prime radicalC23×C113C2×C8
cosocleC2×#11744751C23
hypercenterC22×C8#90673
hypocenterC113C2×#346
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C22×C8

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20712);