Finite Group Databasebeta

C2×#31798172 #47975565

order35104
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#31798172

Splittings

derived, SylowC1097 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4#17984203
commutator, hypocenterC1097C22×C8
FrattiniC2C22×#17984203
FittingC2×C4×C1097C4
socleC22×C1097C2×C4
prime radicalC22×D1097C4
cosocleDic1097C23
LCSG ▷ C1097
UCSC1 ◁ C2×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17552

Conjugacy classes & character table

2224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35104, 229);