Finite Group Databasebeta

C2×#24905749 #35370000

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24905749

Splittings

FittingC2×#322×C83 ⋊ C2
SylowC83 ⋊ C2×#1451

Subgroups

subgroupG/H
centerC2×C42C22×D83
commutatorC22×C83C22×C42
FrattiniC42C23×D83
FittingC2×#322×C83C2
socleC23×C83C2×C42
prime radicalC23×D83C42
cosocleC42×C83C24
hypercenterC2×#322D83
hypocenterC83C2×#1451
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C42 ◁ C2×#322

966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 135164);