Finite Group Databasebeta

C2×#24913068 #35575790

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#24913068

Splittings

SylowC83 ⋊ C2×#2602

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
Fitting, prime radicalC2×#392×C83C2
socleC24×C83C24
hypercenterC2×#392D83
hypocenterC83C2×#2602
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#392

3330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 340954);