Finite Group Databasebeta

C22×#19128063 #36273615

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22×#19128063

Splittings

FittingC22×C4⋊Q8×C83 ⋊ C2
SylowC83 ⋊ C22×#489

Subgroups

subgroupG/H
centerC24C2×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC22×C4⋊Q8×C83C2
socleC24×C83C2×D4
prime radicalC23×D332C22
hypercenterC22×C4⋊Q8D83
hypocenterC83C22×#489
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

2486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1038779);