Finite Group Databasebeta

Q8×#14523959 #30872390

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#14523959

Splittings

FittingQ8×M16×C67 ⋊ C2
SylowC67 ⋊ Q8×#100

Subgroups

subgroupG/H
centerC22C22×(C2×D67)⋊C4
commutatorC23×C67C23×C4
FrattiniC22×C4C23×D67
FittingQ8×M16×C67C2
socleC22×C67C22×C22⋊C4
prime radicalC22×D268C23
cosocleC22×C4×C67C24
hypercenterQ8×M16D67
hypocenterC67Q8×#100
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

1198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1705 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 186127);