Finite Group Databasebeta

C2×#24905327 #35294243

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#24905327

Splittings

SylowC83 ⋊ C2×#1288

Subgroups

subgroupG/H
centerC23C83⋊#95
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC2×#383×C83C2
socleC23×C83#95
prime radicalC24×C83C22⋊C4
cosocleC2×C42×C83C23
hypercenterC2×#383D83
hypocenterC83C2×#1288
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#383

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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, 59407);