Finite Group Databasebeta

C2×#22582867 #31823980

order17984
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#22582867

Splittings

FittingC2×C42×C281 ⋊ C2
SylowC281 ⋊ C2×#124

Subgroups

subgroupG/H
centerC23C22×D281
commutator, cosocleC22×C281C24
FrattiniC22C23×D281
FittingC2×C42×C281C2
socleC23×C281C23
prime radicalC22×D1124C2
hypercenterC2×C42D281
hypocenterC281C2×#124
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×C42

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

4508 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#49093654, #49093656, C2×#31823202, …
maximal normal subgroup of#49093654, #49093656, C2×#31823202, …
maximal quotient ofC2×#31823329, C2×#31823354, C2×#31823365, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 1066);