Finite Group Databasebeta

C2×#20298556 #28398989

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20298556

Splittings

SylowC113 ⋊ C2×#405

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C22×C42
FrattiniC2×C4C23×D113
FittingC22×M16×C113C2
socleC23×C113C22×C4
prime radicalC24×C113C2×C4
cosocleC2×C4×C113C24
hypercenterC22×M16D113
hypocenterC113C2×#405
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C22×M16

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12925);