Finite Group Databasebeta

D17×#485 #14538672

order2176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productD17×#485

Splittings

FittingC17×#485 ⋊ C2
SylowC17 ⋊ C2×#485

Subgroups

subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#485C2
socleC22×C17C22×D4
prime radicalC23×D17D4
hypercenter#485D17
hypocenterC17C2×#485
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D17×#485, D17×#3091, D17×#3093, …
maximal normal subgroup ofC2×D17×#485, D17×#3091, D17×#3093, …
maximal quotient ofD17×#1825, D17×#1854, D17×#1873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 14398);