Finite Group Databasebeta

M32×#3622 #16943301

order4352
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8

Aliases

direct productM32×#3622

Splittings

SylowC17 ⋊ C8×M32

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D17
commutatorC2×C17C2×C82
FittingC4×C17×M32C2
socleC22×C17C2×C4×C8
prime radicalC23×C17C4×C8
cosocleC4×C8×C17C23
hypercenterC4×M32D17
hypocenterC17C8×M32
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C8 ◁ C4×M32

354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 78545);