Finite Group Databasebeta

C2×#20298426 #28392354

order14464
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20298426

Splittings

SylowC113 ⋊ C2×#367

Subgroups

subgroupG/H
centerC23D904
commutatorC8×C113C22×C4
FrattiniC2×C8C22×D113
FittingC22×C16×C113C2
socle, prime radicalC23×C113D8
cosocleC2×C8×C113C23
hypercenterC22×C16D113
hypocenterC113C2×#367
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

3628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6290);