Finite Group Databasebeta

#575×D113 #28405316

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#575×D113

Splittings

Fitting#575×C113 ⋊ C2
SylowC113 ⋊ C2×#575

Subgroups

subgroupG/H
centerC4C2×D4×D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
Fitting#575×C113C2
socleC2×C113C23×D4
hypercenter#575D113
hypocenterC113C2×#575
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19252);