Finite Group Databasebeta

#106×D229 #28411510

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

Aliases

direct product#106×D229

Splittings

Fitting#106×C229 ⋊ C2
SylowC229 ⋊ C2×#106

Subgroups

subgroupG/H
centerC22D4×D229
commutatorC4×C229C22×C4
FrattiniC2×C4C22×D229
Fitting#106×C229C2
socleC22×C229C2×D4
prime radicalC22×D229D4
cosocleC2×C4×C229C23
hypercenter#106D229
hypocenterC229C2×#106
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 578);