Finite Group Databasebeta

#41×Dic389 #38734570

order24896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic389

Splittings

SylowC389 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D389
commutatorC2×C389C23×C4
FrattiniC22C23×D389
Fitting, prime radicalC2×#41×C389C2
socle, cosocleC22×C389C24
hypercenterC2×#41D389
hypocenterC389C4×#41
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

3920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1020);