Finite Group Databasebeta

C22×#11763104 #17901807

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11763104

Splittings

SylowC17 ⋊ C22×#477

Subgroups

subgroupG/H
centerC24C2×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C4×Q8×C17C2
socle, prime radicalC24×C17C2×D4
hypercenterC22×C4×Q8D17
hypocenterC17C22×#477
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×Q8

2358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1037051);