Finite Group Databasebeta

C23×D4×Dic17 #17940889

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×D4×Dic17

Splittings

SylowC17 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
Fitting, prime radicalC24×D4×C17C2
socleC25×C17C23
cosocleC22×C17C26
hypercenterC24×D4D17
hypocenterC17C23×C4×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C24×D4

19998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076133);