Finite Group Databasebeta

C2×#30658155 #45682437

order32992
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30658155

Splittings

FittingC2×Q8×C1031 ⋊ C2
SylowC1031 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D1031
commutator, cosocleC4×C1031C23
FrattiniC4C22×D1031
FittingC2×Q8×C1031C2
socleC22×C1031D4
prime radicalC2×D4124C2
hypercenterC2×Q8D1031
hypocenterC1031C2×SD16
LCSG ▷ C4×C1031 ▷ C2×C1031 ▷ C1031
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16496

Conjugacy classes & character table

5164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32992, 159);