Finite Group Databasebeta

C23×Dic778 #38734923

order24896
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic778

Splittings

SylowC389 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC24C2×D389
commutator, cosocleC2×C389C25
FrattiniC2C24×D389
FittingC23×C4×C389C2
socle, prime radicalC24×C389C22
hypercenterC23×C4D389
hypocenterC389C23×Q8
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C24 ◁ C23×C4

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

6248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1373);