Finite Group Databasebeta

C22×#16864121 #31762873

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

Aliases

direct productC22×#16864121

Splittings

SylowC67 ⋊ C22×#557

Subgroups

subgroupG/H
centerC24C23×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×C4⋊Q8×C67C2
socle, prime radicalC24×C67C24
hypercenterC22×C4⋊Q8D67
hypocenterC67C22×#557
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

7414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

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, 1076610);