Finite Group Databasebeta

C4×#125×D17 #17192809

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#125×D17

Splittings

FittingC4×C17×#125 ⋊ C2
SylowC17 ⋊ C2×C4×#125

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC4×C17×#125C2
socle, cosocleC23×C17C25
prime radicalC23×D17C24
hypercenterC4×#125D17
hypocenterC17C2×C4×#125
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×#125

2622 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, 328053);