Finite Group Databasebeta

C2×#24909437 #35558338

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#24909437

Splittings

FittingC2×#361×C83 ⋊ C2
SylowC83 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC22#19127836
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC2×#361×C83C2
socleC22×C83#447
prime radicalC2×#19128502C2
hypercenterC2×#361D83
hypocenterC83C2×#2194
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 323502);