Finite Group Databasebeta

M32×#3624 #17957983

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

Aliases

direct productM32×#3624

Splittings

SylowC17 ⋊ C8×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#595
commutatorC2×C17C2×C82
FittingC2×C17×M32C4
socleC22×C17C2×C4×C8
prime radicalC23×C17C4×C8
cosocleC8×Dic17C23
hypercenterC2×M32#595
hypocenterC17C8×M32
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×M32

354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093227);