Finite Group Databasebeta

C2×#24912831 #35575730

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

Aliases

direct productC2×#24912831

Splittings

SylowC83 ⋊ C2×#2581

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#389×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#389D83
hypocenterC83C2×#2581
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

2614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 340894);