Finite Group Databasebeta

Q8×(C2×D59)⋊C8 #28605202

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×(C2×D59)⋊C8

Splittings

FittingC2×C8×Q8×C59 ⋊ C2
SylowC59 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D59
commutatorC22×C59C23×C8
FittingC2×C8×Q8×C59C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenterC2×C8×Q8D59
hypocenterC59Q8×C22⋊C8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 186081);