Finite Group Databasebeta

C2×#20299475 #28406269

order14464
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20299475

Splittings

FittingC2×C22⋊C4×C113 ⋊ C4
SylowC113 ⋊ C2×#342

Subgroups

subgroupG/H
centerC22(C2×#90673)⋊C4
commutatorC22×C113C2×C42
FrattiniC23C22×#90673
FittingC2×C22⋊C4×C113C4
socleC22×C113#95
prime radicalC24×D113C22
cosocleC23×D113C23
hypercenterC2×C22⋊C4#90673
hypocenterC113C2×#342
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20205);