Finite Group Databasebeta

C22×#106×D17 #17897964

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#106×D17

Splittings

FittingC22×C17×#106 ⋊ C2
SylowC17 ⋊ C23×#106

Subgroups

subgroupG/H
centerC24D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C17×#106C2
socleC24×C17C2×D4
prime radicalC24×D17D4
cosocleC2×C4×C17C25
hypercenterC22×#106D17
hypocenterC17C23×#106
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

3614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033208);