Finite Group Databasebeta

C22×D8×Dic17 #17898326

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

Aliases

direct productC22×D8×Dic17

Splittings

SylowC17 ⋊ C22×C4×D8

Subgroups

subgroupG/H
centerC24D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
Fitting, prime radicalC23×D8×C17C2
socleC24×C17C2×D4
cosocleC2×C4×C17C25
hypercenterC23×D8D17
hypocenterC17C22×C4×D8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

3694 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, 1033570);