Finite Group Databasebeta

C2×C4×D4×D113 #28403741

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4×D4×D113

Splittings

FittingC2×C4×D4×C113 ⋊ C2
SylowC113 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C24×C4
FrattiniC22C24×D113
FittingC2×C4×D4×C113C2
socleC23×C113C24
prime radicalC22×D4×D113C2
cosocleC22×C113C25
hypercenterC2×C4×D4D113
hypocenterC113C22×C4×D4
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

2528 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, 17677);