Finite Group Databasebeta

C2×#31798809 #47977033

order35296
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31798809

Splittings

FittingC2×Q8×C1103 ⋊ C2
SylowC1103 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D1103
commutator, cosocleC4×C1103C23
FrattiniC4C22×D1103
FittingC2×Q8×C1103C2
socleC22×C1103D4
prime radicalC2×D4412C2
hypercenterC2×Q8D1103
hypocenterC1103C2×SD16
LCSG ▷ C4×C1103 ▷ C2×C1103 ▷ C1103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17648

Conjugacy classes & character table

5524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35296, 159);