Finite Group Databasebeta

#428×D113 #28399155

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#428×D113

Splittings

Fitting#428×C113 ⋊ C2
SylowC113 ⋊ C2×#428

Subgroups

subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#428×C113C2
socleC22×C113C22×D4
prime radicalC23×D113D4
cosocleC2×C4×C113C24
hypercenter#428D113
hypocenterC113C2×#428
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

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, 13091);