Finite Group Databasebeta

Q8×C59⋊C8 #16837528

order3776
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productQ8×C59⋊C8

Splittings

SylowC59 ⋊ C8×Q8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D59
commutatorC2×C59C22×C8
FittingC4×Q8×C59C2
socle, prime radicalC22×C59C22×C4
cosocleC2×C4×C59C23
hypercenterC4×Q8D59
hypocenterC59C8×Q8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×Q8

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 675);