Finite Group Databasebeta

C2×#24905371 #35294765

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#24905371

Splittings

SylowC83 ⋊ C2×#1306

Subgroups

subgroupG/H
centerC23C83⋊#95
commutatorC23×C83C2×C42
FrattiniC23×C4C22×D83
FittingC2×#381×C83C2
socleC23×C83#95
prime radicalC25×C83C2×C4
cosocleC23×C4×C83C23
hypercenterC2×#381D83
hypocenterC83C2×#1306
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 59929);