Finite Group Databasebeta

C2×#20298571 #28399030

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20298571

Splittings

FittingC2×#117×C113 ⋊ C2
SylowC113 ⋊ C2×#410

Subgroups

subgroupG/H
centerC2×C4#14268624
commutatorC22×C113C23×C4
FrattiniC23C23×D113
FittingC2×#117×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×#14268647C2
cosocleC23×C113C24
hypercenterC2×#117D113
hypocenterC113C2×#410
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12966);