Finite Group Databasebeta

C2×#30681223 #46777696

order33632
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30681223

Splittings

SylowC1051 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D1051
commutator, cosocleC4×C1051C23
FrattiniC4C22×D1051
FittingC2×Q8×C1051C2
socle, prime radicalC22×C1051D4
hypercenterC2×Q8D1051
hypocenterC1051C2×Q16
LCSG ▷ C4×C1051 ▷ C2×C1051 ▷ C1051
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33632

Conjugacy classes & character table

5264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33632, 163);