Finite Group Databasebeta

C2×#20300920 #28411512

order14656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20300920

Splittings

SylowC229 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23D916
commutatorC4×C229C22×C4
FrattiniC2×C4C22×D229
FittingC22×C8×C229C2
socle, prime radicalC23×C229D4
cosocleC2×C4×C229C23
hypercenterC22×C8D229
hypocenterC229C2×#106
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

Conjugacy classes & character table

3676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 580);