Finite Group Databasebeta

C2×#20298614 #28399115

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20298614

Splittings

FittingC22×M16×C113 ⋊ C2
SylowC113 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC22×M16×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×#14268647C2
cosocleC2×C4×C113C24
hypercenterC22×M16D113
hypocenterC113C2×#421
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

772 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, 13051);