Finite Group Databasebeta

Q8×C22⋊C4×D59 #28747874

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productQ8×C22⋊C4×D59

Splittings

FittingQ8×C22⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingQ8×C22⋊C4×C59C2
socle, cosocleC23×C59C25
prime radicalC24×D59C23
hypercenterQ8×C22⋊C4D59
hypocenterC59C2×Q8×C22⋊C4
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328753);