Finite Group Databasebeta

C2×Q32×Dic17 #17187599

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q32×Dic17

Splittings

SylowC17 ⋊ C2×C4×Q32

Subgroups

subgroupG/H
centerC23D8×D17
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC22×C17×Q32C2
socle, prime radicalC23×C17C2×D8
cosocleC2×C8×C17C24
hypercenterC22×Q32D17
hypocenterC17C2×C4×Q32
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322843);