Finite Group Databasebeta

C2×C22⋊C8×D113 #28399004

order14464
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D113

Splittings

FittingC2×C22⋊C8×C113 ⋊ C2
SylowC113 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C23×C8
FrattiniC2×C4C23×D113
FittingC2×C22⋊C8×C113C2
socleC23×C113C22×C4
prime radicalC24×D113C4
cosocleC2×C4×C113C24
hypercenterC2×C22⋊C8D113
hypocenterC113C22×C22⋊C8
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12940);