Finite Group Databasebeta

M32×Dic134 #31009344

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productM32×Dic134

Splittings

SylowC67 ⋊ Q8×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D67
commutator, socleC22×C67C23×C8
FittingC4×M32×C67C2
prime radicalC23×C67C22×C8
cosocleC2×C8×C67C24
hypercenterC4×M32D67
hypocenterC67Q8×M32
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C8 ◁ C4×M32

530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323081);