Finite Group Databasebeta

C2×#20299599 #28407207

order14464
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20299599

Splittings

SylowC113 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×#90673
commutatorC2×C113C23×C8
FrattiniC22C23×#90673
FittingC2×C42×C113C4
socleC23×C113C22×C4
prime radicalC23×D113C2×C4
cosocleC2×Dic113C24
hypercenterC2×C42#90673
hypocenterC113C22×C4⋊C8
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C42

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21143);