Finite Group Databasebeta

C2×#99×D113 #28399025

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#99×D113

Splittings

FittingC2×#99×C113 ⋊ C2
SylowC113 ⋊ C22×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
FittingC2×#99×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D4×D113C2
cosocleC23×C113C24
hypercenterC2×#99D113
hypocenterC113C22×#99
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

1112 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, 12961);