Finite Group Databasebeta

#568×D113 #28405281

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#568×D113

Splittings

Fitting#568×C113 ⋊ C2
SylowC113 ⋊ C2×#568

Subgroups

subgroupG/H
center, FrattiniC4C24×D113
commutator, socleC2×C113C24×C4
Fitting#568×C113C2
prime radicalC2×#41×D113C2
cosocleC4×C113C25
hypercenter#568D113
hypocenterC113C2×#568
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ #568

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19217);