Finite Group Databasebeta

C2×C4×#16862558 #46800706

order33952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#16862558
unambiguous semidirect productD1061⋊C42

Splittings

FittingC2×C4×C1061 ⋊ C4
derived, SylowC1061 ⋊ C2×C42

Subgroups

subgroupG/H
center, hypercenterC2×C4#16862558
commutator, hypocenterC1061C2×C42
FrattiniC2C22×#16862558
FittingC2×C4×C1061C4
socleC22×C1061C2×C4
prime radicalC22×D1061C22
cosocleC2×D1061C23
LCSG ▷ C1061
UCSC1 ◁ C2×C4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8488

Conjugacy classes & character table

2152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 222);