Finite Group Databasebeta

C2×#24906912 #35386703

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

Aliases

direct productC2×#24906912

Splittings

SylowC83 ⋊ C2×#1683

Subgroups

subgroupG/H
centerC23#14581764
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×#474×C83C2
socleC23×C83#121
prime radicalC22×D4×C83D4
hypercenterC2×#474D83
hypocenterC83C2×#1683
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1616 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 151867);