Finite Group Databasebeta

C4×#11763031 #17040559

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

Aliases

direct productC4×#11763031

Splittings

FittingC42×Q8×C17 ⋊ C2
SylowC17 ⋊ C4×#464

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC42×Q8×C17C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenterC42×Q8D17
hypocenterC17C4×#464
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×Q8

1016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 175803);