Finite Group Databasebeta

C2×#31798174 #47975568

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

Aliases

direct productC2×#31798174

Splittings

SylowC1097 ⋊ C2×M16

Subgroups

subgroupG/H
centerC22C2×#17984203
commutatorC2×C1097C22×C4
FrattiniC2C22×#17984203
FittingC2×C4×C1097C4
socleC22×C1097C2×C4
prime radicalC22×D1097C4
cosocleDic1097C23
hypercenterC2×C4#17984203
hypocenterC1097C2×M16
LCSG ▷ C2×C1097 ▷ C1097
UCSC1 ◁ C22 ◁ C2×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17552

Conjugacy classes & character table

2212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35104, 232);