Finite Group Databasebeta

C2×#24915750 #35610241

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#24915750

Splittings

SylowC83 ⋊ C2×#2848

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC25×C4×C83C2
socleC24×C83C24
prime radicalC26×C83C22
hypercenterC25×C4D83
hypocenterC83C2×#2848
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C25×C4

7502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

5336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 375405);