Finite Group Databasebeta

C2×#20299625 #28407276

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

Aliases

direct productC2×#20299625

Splittings

SylowC113 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC23C22×#90673
commutatorC2×C113C23×C8
FrattiniC22C23×#90673
FittingC2×C22⋊C4×C113C4
socleC23×C113C22×C4
prime radicalC22×C22⋊D113C4
cosocleC2×Dic113C24
hypercenterC2×C22⋊C4#90673
hypocenterC113C2×C8×D4
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C22⋊C4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21212);