Finite Group Databasebeta

C2×#24911907 #35574182

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

Aliases

direct productC2×#24911907

Splittings

FittingC22×#95×C83 ⋊ C2
SylowC83 ⋊ C2×#2498

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×#95×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC22×#95D83
hypocenterC83C2×#2498
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×#95

3114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 339346);