Finite Group Databasebeta

C2×#30684093 #46800581

order33952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#30684093

Splittings

FittingC22×C4×C1061 ⋊ C2
SylowC1061 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1061
commutatorC2×C1061C22×C4
FrattiniC22C22×D1061
FittingC22×C4×C1061C2
socleC23×C1061C22
prime radicalC23×D1061C2
cosocleC22×C1061C23
hypercenterC22×C4D1061
hypocenterC1061C2×C22⋊C4
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16976

Conjugacy classes & character table

8500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 97);