Finite Group Databasebeta

C2×#24909802 #35562587

order21248
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#24909802

Splittings

FittingC2×#376×C83 ⋊ C2
SylowC83 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D83
commutatorC2×C83C23×C42
FrattiniC23C24×D83
FittingC2×#376×C83C2
socleC24×C83C24
prime radicalC24×D83C23
cosocleC23×C83C25
hypercenterC2×#376D83
hypocenterC83C2×C4×#117
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×#376

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 327751);