Finite Group Databasebeta

C22×#11763051 #17901423

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763051

Splittings

FittingC22×C17×#107 ⋊ C2
SylowC17 ⋊ C22×#467

Subgroups

subgroupG/H
centerC24D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#107C2
socleC24×C17C2×D4
prime radicalC24×D17D4
hypercenterC22×#107D17
hypocenterC17C22×#467
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036667);