Finite Group Databasebeta

C2×#30628465 #44537980

order31456
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30628465

Splittings

SylowC983 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D983
commutator, cosocleC4×C983C23
FrattiniC4C22×D983
FittingC2×Q8×C983C2
socle, prime radicalC22×C983D4
hypercenterC2×Q8D983
hypocenterC983C2×Q16
LCSG ▷ C4×C983 ▷ C2×C983 ▷ C983
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31456

Conjugacy classes & character table

4924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 163);