Finite Group Databasebeta

C2×#31798151 #47975495

order35104
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31798151

Splittings

FittingC2×Q8×C1097 ⋊ C2
SylowC1097 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D1097
commutator, cosocleC4×C1097C23
FrattiniC4C22×D1097
FittingC2×Q8×C1097C2
socleC22×C1097D4
prime radicalC2×D4388C2
hypercenterC2×Q8D1097
hypocenterC1097C2×SD16
LCSG ▷ C4×C1097 ▷ C2×C1097 ▷ C1097
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17552

Conjugacy classes & character table

5494 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35104, 159);