Finite Group Databasebeta

Q8×C22⋊(C67⋊C8) #30872347

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×C22⋊(C67⋊C8)

Splittings

SylowC67 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D67
commutatorC22×C67C23×C8
FittingC22×C4×Q8×C67C2
socleC23×C67C23×C4
prime radicalC24×C67C22×C4
cosocleC22×C4×C67C24
hypercenterC22×C4×Q8D67
hypocenterC67Q8×C22⋊C8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

1356 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, 186084);