Finite Group Databasebeta

#418×D113 #28399072

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

Aliases

direct product#418×D113

Splittings

Fitting#418×C113 ⋊ C2
SylowC113 ⋊ C2×#418

Subgroups

subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×D113C2
cosocleC2×C4×C113C24
hypercenter#418D113
hypocenterC113C2×#418
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

1008 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, 13008);