Finite Group Databasebeta

C2×#20300923 #28411526

order14656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20300923

Splittings

SylowC229 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D229
commutatorC4×C229C22×C4
FrattiniC2×C4C22×D229
FittingC2×M16×C229C2
socleC22×C229C4⋊C4
prime radicalC23×C229Q8
cosocleC2×C4×C229C23
hypercenterC2×M16D229
hypocenterC229C2×#108
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

2308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 594);