Finite Group Databasebeta

C2×#24918969 #36279381

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#24918969

Splittings

SylowC83 ⋊ C2×#3266

Subgroups

subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
Fitting, prime radicalC2×#546×C83C2
socleC23×C83C22×D4
hypercenterC2×#546D83
hypocenterC83C2×#3266
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

2882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1044545);