Finite Group Databasebeta

#410×D113 #28399028

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

Aliases

direct product#410×D113

Splittings

Fitting#410×C113 ⋊ C2
SylowC113 ⋊ C2×#410

Subgroups

subgroupG/H
centerC4C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
Fitting#410×C113C2
socleC2×C113C22×C22⋊C4
prime radicalC2×#41×D113C2
cosocleC23×C113C24
hypercenter#410D113
hypocenterC113C2×#410
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

788 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, 12964);