Finite Group Databasebeta

C24×Dic226 #28405369

order14464
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC24×Dic226

Splittings

SylowC113 ⋊ C24×Q8

Subgroups

subgroupG/H
centerC25C2×D113
commutator, cosocleC2×C113C26
FrattiniC2C25×D113
FittingC24×C4×C113C2
socle, prime radicalC25×C113C22
hypercenterC24×C4D113
hypocenterC113C24×Q8
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C25 ◁ C24×C4

6264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

3664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19305);