Finite Group Databasebeta

C2×#20298471 #28392985

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20298471

Splittings

SylowC113 ⋊ C2×#385

Subgroups

subgroupG/H
centerC24C22×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
FittingC24×C4×C113C2
socleC24×C113C23
prime radicalC25×C113C22
cosocleC23×C113C24
hypercenterC24×C4D113
hypocenterC113C2×#385
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C24 ◁ C24×C4

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6921);