Finite Group Databasebeta

C22×#16864132 #31762883

order17152
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#16864132

Splittings

SylowC67 ⋊ C22×#559

Subgroups

subgroupG/H
centerC24C23×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
Fitting, prime radicalC22×#127×C67C2
socleC24×C67C24
hypercenterC22×#127D67
hypocenterC67C22×#559
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×#127

8710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1076620);