Finite Group Databasebeta

C2×#20298364 #28390303

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

Aliases

direct productC2×#20298364

Splittings

SylowC113 ⋊ C2×#342

Subgroups

subgroupG/H
centerC23#14268624
commutatorC22×C113C2×C42
FrattiniC24C22×D113
FittingC22×C22⋊C4×C113C2
socleC23×C113C22⋊C4
prime radicalC25×C113C22
cosocleC24×C113C23
hypercenterC22×C22⋊C4D113
hypocenterC113C2×#342
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

680 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, 4239);