Finite Group Databasebeta

C2×#24905361 #35294659

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#24905361

Splittings

SylowC83 ⋊ C2×#1302

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic83
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC2×#432×C83C2
socleC23×C83#95
prime radicalC24×C83C4⋊C4
cosocleC2×C42×C83C23
hypercenterC2×#432D83
hypocenterC83C2×#1302
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#432

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

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, 59823);