Finite Group Databasebeta

C2×#24905351 #35294544

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

Aliases

direct productC2×#24905351

Splittings

SylowC83 ⋊ C2×#1298

Subgroups

subgroupG/H
centerC22×C4(C2×D83)⋊C4
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC22×C22⋊C8×C83C2
socleC23×C83#95
prime radicalC25×C83Q8
cosocleC23×C4×C83C23
hypercenterC22×C22⋊C8D83
hypocenterC83C2×#1298
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 59708);