Finite Group Databasebeta

C4×#11763285 #17192573

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#11763285

Splittings

FittingC42×Q8×C17 ⋊ C2
SylowC17 ⋊ C4×#519

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC42×Q8×C17C2
socle, cosocleC23×C17C25
prime radicalC23×D17C24
hypercenterC42×Q8D17
hypocenterC17C4×#519
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C42×Q8

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327817);