Finite Group Databasebeta

C24×Dic334 #36338933

order21376
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC24×Dic334

Splittings

SylowC167 ⋊ C24×Q8

Subgroups

subgroupG/H
centerC25C2×D167
commutator, cosocleC2×C167C26
FrattiniC2C25×D167
FittingC24×C4×C167C2
socle, prime radicalC25×C167C22
hypercenterC24×C4D167
hypocenterC167C24×Q8
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C25 ◁ C24×C4

6264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21376

Conjugacy classes & character table

5392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 19305);