Finite Group Databasebeta

#46800586

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

Aliases

No aliases for this group.

Splittings

SylowC1061 ⋊ #117

Subgroups

subgroupG/H
center, FrattiniC22C22×D1061
commutatorC2×C1061C22×C4
FittingC22⋊C4×C1061C2
socle, cosocleC22×C1061C23
prime radicalC23×C1061C22
hypercenterC22⋊C4D1061
hypocenterC1061#117
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C22 ◁ C22⋊C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16976

Polycyclic presentation:

2^5,1061|a^2=e,c^2=d,b^a=bd,f^c=f^1060

Conjugacy classes & character table

5320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 102);