Finite Group Databasebeta

C2×Dic1051⋊C4 #46777633

order33632
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×Dic1051⋊C4

Splittings

SylowC1051 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D1051
commutatorC2×C1051C22×C4
FrattiniC22C22×D1051
FittingC22×C4×C1051C2
socle, prime radicalC23×C1051C22
cosocleC22×C1051C23
hypercenterC22×C4D1051
hypocenterC1051C2×C4⋊C4
LCSG ▷ C2×C1051 ▷ C1051
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33632

Conjugacy classes & character table

8420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33632, 100);