Finite Group Databasebeta

C2×#24907906 #35406157

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#24907906

Splittings

FittingC23×C42×C83 ⋊ C2
SylowC83 ⋊ C2×#1896

Subgroups

subgroupG/H
centerC22×C4C2×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC23×C42×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC2×#19128212C2
cosocleC22×C4×C83C24
hypercenterC23×C42D83
hypocenterC83C2×#1896
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×C42

2514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

5336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 171321);