Finite Group Databasebeta

C2×#20298553 #28398986

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

Aliases

direct productC2×#20298553

Splittings

SylowC113 ⋊ C2×#405

Subgroups

subgroupG/H
centerC22×C8C2×D113
commutatorC2×C113C22×C42
FrattiniC2×C4C23×D113
FittingC23×C8×C113C2
socleC23×C113C22×C4
prime radicalC24×C113C2×C4
cosocleC2×C4×C113C24
hypercenterC23×C8D113
hypocenterC113C2×#405
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C8 ◁ C23×C8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12922);