Finite Group Databasebeta

C4×#11762611 #16949529

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11762611

Splittings

FittingC2×C4×C16×C17 ⋊ C2
SylowC17 ⋊ C4×#357

Subgroups

subgroupG/H
centerC22×C4D136
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC2×C4×C16×C17C2
socleC23×C17C2×D8
prime radicalC22×D136C22
cosocleC22×C8×C17C23
hypercenterC2×C4×C16D17
hypocenterC17C4×#357
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84773);