Finite Group Databasebeta

C2×#24909033 #35434306

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24909033

Splittings

SylowC83 ⋊ C2×#2101

Subgroups

subgroupG/H
centerC24D4×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×#340×C83C2
socle, prime radicalC24×C83C2×D4
hypercenterC2×#340D83
hypocenterC83C2×#2101
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 199470);