Finite Group Databasebeta

#417×D113 #28399082

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#417×D113

Splittings

Fitting#417×C113 ⋊ C2
SylowC113 ⋊ C2×#417

Subgroups

subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×D113C2
cosocleC2×C4×C113C24
hypercenter#417D113
hypocenterC113C2×#417
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

816 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, 13018);