Finite Group Databasebeta

C4×#11762563 #16939470

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11762563

Splittings

SylowC17 ⋊ C4×#336

Subgroups

subgroupG/H
centerC22×C42C2×D17
commutatorC2×C17C42×C8
FrattiniC23×C4C22×D17
FittingC22×C4×C8×C17C2
socle, prime radicalC24×C17C22×C4
cosocleC23×C4×C17C23
hypercenterC22×C4×C8D17
hypocenterC17C4×#336
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 74714);