Finite Group Databasebeta

C2×#24921272 #36312584

order21248
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#24921272

Splittings

FittingC2×Q82×C83 ⋊ C2
SylowC83 ⋊ C2×#3502

Subgroups

subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×Q82×C83C2
socleC23×C83C25
prime radicalC23×D83C24
hypercenterC2×Q82D83
hypocenterC83C2×#3502
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×Q82

6826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1077748);