Finite Group Databasebeta

C2×#31798141 #47975433

order35104
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#31798141

Splittings

FittingC22×C4×C1097 ⋊ C2
SylowC1097 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1097
commutatorC2×C1097C22×C4
FrattiniC22C22×D1097
FittingC22×C4×C1097C2
socleC23×C1097C22
prime radicalC23×D1097C2
cosocleC22×C1097C23
hypercenterC22×C4D1097
hypocenterC1097C2×C22⋊C4
LCSG ▷ C2×C1097 ▷ C1097
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17552

Conjugacy classes & character table

8788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35104, 97);