Finite Group Databasebeta

Q8×C4⋊(C67⋊C8) #30874625

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productQ8×C4⋊(C67⋊C8)

Splittings

SylowC67 ⋊ Q8×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D67
commutatorC22×C67C23×C8
FittingC42×Q8×C67C2
socle, prime radicalC23×C67C23×C4
cosocleC22×C4×C67C24
hypercenterC42×Q8D67
hypocenterC67Q8×C4⋊C8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C42×Q8

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

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, 188362);