Finite Group Databasebeta

C2×#30684380 #46801212

order34016
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30684380

Splittings

SylowC1063 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D1063
commutator, cosocleC4×C1063C23
FrattiniC4C22×D1063
FittingC2×Q8×C1063C2
socle, prime radicalC22×C1063D4
hypercenterC2×Q8D1063
hypocenterC1063C2×Q16
LCSG ▷ C4×C1063 ▷ C2×C1063 ▷ C1063
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34016

Conjugacy classes & character table

5324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34016, 163);