Finite Group Databasebeta

← Prev (#28399126) Next (#28399128) →

C2×#20298620 #28399127

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

Aliases

direct productC2×#20298620

Splittings

FittingC2×C4⋊C8×C113 ⋊ C2
SylowC113 ⋊ C2×#423

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
FittingC2×C4⋊C8×C113C2
socleC23×C113C22×C4
prime radicalC23×D113C2×C4
cosocleC2×C4×C113C24
hypercenterC2×C4⋊C8D113
hypocenterC113C2×#423
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13063);