Finite Group Databasebeta

C2×#41×Dic113 #28403756

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×Dic113

Splittings

SylowC113 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C24×C4
FrattiniC22C24×D113
Fitting, prime radicalC22×#41×C113C2
socleC23×C113C24
cosocleC22×C113C25
hypercenterC22×#41D113
hypocenterC113C2×C4×#41
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C22×#41

1728 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, 17692);