Finite Group Databasebeta

C2×#20298594 #28399070

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20298594

Splittings

SylowC113 ⋊ C2×#416

Subgroups

subgroupG/H
centerC22×C4C22⋊D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting, prime radicalC22×#41×C113C2
socleC23×C113C2×D4
cosocleC2×C4×C113C24
hypercenterC22×#41D113
hypocenterC113C2×#416
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13006);