Finite Group Databasebeta

C2×C4×#17984203 #47975558

order35104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#17984203
unambiguous semidirect productD1097⋊C42

Splittings

FittingC2×C4×C1097 ⋊ C4
derived, SylowC1097 ⋊ C2×C42

Subgroups

subgroupG/H
center, hypercenterC2×C4#17984203
commutator, hypocenterC1097C2×C42
FrattiniC2C22×#17984203
FittingC2×C4×C1097C4
socleC22×C1097C2×C4
prime radicalC22×D1097C22
cosocleC2×D1097C23
LCSG ▷ C1097
UCSC1 ◁ C2×C4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8776

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, 222);