Finite Group Databasebeta

C24×Dic218 #28377827

order13952
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC24×Dic218

Splittings

SylowC109 ⋊ C24×Q8

Subgroups

subgroupG/H
centerC25C2×D109
commutator, cosocleC2×C109C26
FrattiniC2C25×D109
FittingC24×C4×C109C2
socle, prime radicalC25×C109C22
hypercenterC24×C4D109
hypocenterC109C24×Q8
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C25 ◁ C24×C4

6264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 19305);